PreCalculus

2017-2018

Semester 1

Required materials for mathematics classes
Your school-issued laptop, charged!
Two (2) hardbound theme books (i.e. Mead Composition Book) for journaling (no spirals!).  Use one for homework (enter assignments chronologically) and the other for Journal Reflections (this theme book stays in the classroom).
Texas Instruments TI-83+ (or TI-84+) Graphing Calculator + extra AAA cells.  DO NOT expect the school to provide you extra cells!
Basic drawing supplies (ruler that measures in centimeters, compass, protractor).
Several pencils or mechanical pencil with extra lead + a pen for writing JRs.

Desmos Graphing Calculator.

Join Wolfram Alpha, which provides step-by-step solutions.

 

Greetings
 Date

Entry Task

Activity

Assignment/Homework*

9/6
Find your seat.
Meet your peers & teacher.

Debrief Summer Homework and compile a list of needed review items.

JR: What are your goals in this class for this year?
Complete Getting to Know You.

Download the course Syllabus.  Sign and return the signature sheet.

List in your homework notebook what you believe you know well and what you need to know better.

Bring two hardbound "theme books"--one for journal and one for homework.
9/7
Get ready for the Expectations Quiz.  Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people.
Clarify expectations, both from the class syllabus and the Student Handbook.

JR:  What do you believe will be your biggest challenge this year in PreCalculus?
Graph the Olympic Games data.
9/8
With a table partner, address the following questions
  • Are your graphs fundamentally identical?
  • How confident are you in your prediction of the winning times?
  • What similarities and differences do you see in the men's vs. the women's times?
  • What are some errors students may have made creating these graphs?
Remember to record your responses in your homework notebook!  :-)
Debrief the ET.

Discuss calculator data entry, equation modeling.

JR:  List the mathematics content and processes you believe you command.
Enter the Olympic Games data into your calculator's lists and model as
  • Linear.
  • Power.
  • Exponential.
then use the models to estimate the winning times for 2020 and 2040.  Comment on your confidence in these estimates. Show all your work and explain your process, including what the variables you used represent.
9/11
Why is the exponential model for the Olympic Games data still not realistic? Debrief homework, including entering and analyzing data.

Catch up on JRs.

JR:  List the steps necessary to enter data and model using a calculator.
Enter the Olympic Games data into your calculator's lists and model as
  • Quadratic.
  • Cubic.
  • Quartic.
then use the models to estimate the winning times for 2020 and 2040.  Comment on your confidence in these estimates. Show all your work and explain your process, including what the variables you used represent.
9/12
Answer these questions regarding atmospheric pressure
  • What units are used in the US for atmospheric pressure?
  • What is the value of atmospheric pressure under standard conditions?
  • By what rate does atmospheric pressure decrease with altitude?
  • Why does atmospheric pressure decrease with altitude?
Graph Pressure vs. Altitude (by hand).  Find a part of the data that is approximately linear, draw the line on your graph, and determine the slope of the line.  Note that you are NOT being asked to model the data set nor graph using technology!

JR:  What are some other models for data besides linear, power, and exponential? Explain their similarities and differences.
Finish the graph and question.
9/13 or 9/14
Suggest a method to measure a person's height using meter sticks wherein the least amount of measurement variability is introduced.  You may discuss this with your table partner
Design and execute an investigation that addresses the question "what is the relationship between a person's height and her/his arm span?"

While executing the above investigation, also collect data on forearm length and foot length.

JR:  Which mathematical model do you believe will best fit the relationship between a person's height vs. arm span?  Explain why you believe this.
Graph height vs. arm span.  Create a linear mathematical model that fits the data and use your model to predict the height of a person whose arm span is 200 cm long.
9/15
Get ready for the quiz!  Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people. Quiz.  Expect questions on data modeling.  No calculator or note card.

JR:  Explain how the data collection we performed yesterday could be improved.
Graph forearm length vs. foot length.  Create a mathematical model that fits the data and use your model to predict the forearm length  of a person whose foot length is 28 cm long.
9/18
Work silently and singularly.  For y = 1/2x + 5, compute the value of y when x = 10.
Debrief ET.

Debrief last two HW.

JR:  Explain, as if you were talking to a new arrival to this class, the meaning of "mathematical model."  Give several examples.
Spend at most one hour on the algebra diagnostic test.  Do all work in your homework notebook.
9/19
Rei (pronounced like "Ray") is an outstanding outdoorsman and prides himself on his mathematical understanding.  He says "I just ran up this trail one hundred (100) feet and gained ten (10) feet in elevation.  Slope is rise over run, so the slope of this trail is 0.1 (1 divided by ten)."  Comment on Rei's process and conclusion. Debrief ET.

JR:  Give an example of a trigonometry problem you know how to do.  Demonstrate how to solve it.
Complete the online Trigonometry Test.  Calculator allowed.  Note: this is NOT for a grade--it is a pre-test of your understanding.  Do all problems in your homework notebook and record your score.

Before beginning the test, select "Multiple Choice Test," 42 for "Seed Number," Trigonometry for "Select a Test," 20 for "How Many Problems?" then click "Take the test with problems chosen at random."  When finished, click "Submit Your Work and Get All The Problems Displayed."  Record your score in your homework notebook.
*Unless otherwise noted, homework is due the next class day.



Chapter 5: Trigonometric Functions: Unit Circle Approach
 Date

Entry Task

Activity

Assignment/Homework*

9/20 or 9/21 Bozal borrows a ladder from his neighbor to wash the exterior windows of his house.  He knows the ladder extends to sixteen feet and the window bottom is twelve feet above the ground.  Compute the number of feet the bottom of the ladder must be from the wall to reach the bottom of the window.  What angle does the ladder make with the (level) ground?  How does this compare with OSHA's guideline "The proper angle for setting up a ladder is to place its base a quarter of the working length of the ladder from the wall or other vertical surface?"
Try Angles activity.

Receive textbooks--record your book number in the front of your homework notebook.  Take the textbook home, leave it at home!!!

Report the last three digits of your book number to Dr. Edge.

JR:  Draw three non-right triangles, one acute, one obtuse, and one isosceles.  Perform the same measurements as the Try Angles activity.  Explain your results.
Find a long, straight object, such as a ladder.  Measure its length, then lean it against a wall.  Perform the following measures
1.    The height of the top of the object from the base of the wall.
2.    The distance of the foot of the object from the base of the wall.
3.    The angle the ladder makes with the horizontal surface on which it rests (presumably a floor or the ground).
Compute each of the following
•    The length of the ladder using measures #1 and #2 above.
•    Measure #1 using measure #3 and the known length of the ladder.
Measure #1 using the known length of the ladder and a new measure for #2 that is 20% larger than the previous one.
9/22 Get ready for the quiz!  Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people. Quiz: right triangle trigonometry.  No calculator or note card.  A ruler and protractor are required for this quiz.  NO MATERIALS WILL BE LOANED ONCE CLASS BEGINS!

JR:  Explain how do determine if a triangle, known only by the lengths of its sides, is a right triangle.
Use the values from the online trig tables (NOT from your calculator) to solve the following problems.  Recall you MUST show all parts of your solution process.
  • Solve for the unknown sides and angles of a right triangle if one angle is 35 degrees and the longest side is 12 cm.
  • Solve for the unknown sides and angles of a right triangle if one angle is 15 degrees and the shortest side is 22 cm.
  • Solve for the unknown angles of a triangle if the sides are 15, 36, and 39 cm.
9/25
Determine in which quadrant each of the following angles is located and compute the angle made by moving clockwise (therefore, a negative angle) that is equivalent
  • 25°'
  • 110°
  • 165°
  • 265°
  • 310°
  • 330°
Partner challenge: with one table partner, create a problem like those from the homework then trade your problems.  Calculators may be used but only for arithmetic (not the trig functions).

JR:  Explain how to determine an angle measure knowing only the lengths of two sides of a right triangle.  Assume you are not allowed to use the trig functions on a calculator or computer.  Hint, consider the online trig tables.  :-)
Create scale models of each of the triangles from Friday's homework.  Measure sides to within one centimeter and angles to within one degree.
9/26
Explain the meaning of "radian" as related to angle measure.
Explore the Radian Measure Activity on Desmos.

JR:  Explain the relationship between measuring angles in degrees vs. radians.  Include a diagram and equation that will translate radians into degrees.
p. 408 #23, 25, 27, 35.
9/27 or 9/28
We have heard the phrase "Unit Circle" many times this year already.  What does it mean?
Can You Do The Can Can? activity.

JR:  Explain how today's activity is related to trigonometry.  Include a diagram.
p. 408 #55 - 58.  Include the diagram!
9/29
Get ready for the quiz!  Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people. Quiz: trigonometric ratios.  You may use a calculator, ruler, protractor, and your paper from the Can You Do The Can Can? activity.

JR:  Examine the box at the bottom of p. 409 (Definition of the Trigonometric Function).  Why are the definitions of the functions NOT ratios?
Copy (by hand) Table 1 on p. 410 (Special Values of the Trigonometric Functions) into your homework notebook.  Include the diagram.
10/2
Prove sin2(x) + cos2(x) = 1.
Fun with a Calculator activity.

JR:  Examine the box on p. 415 (Fundamental Identities).  Copy the identities.
pp. 416-417 #3-4; 37-44.
10/3
Compare your processes for solving #37-44 with your table partner.  Explain (in your homework notebook) why they asked for two answers. Work p. 418 #63-70, 80-81.

JR:  What is a reasonable decimal equivalent to a time of 0748?
Prepare to graph (on paper) 0 through 730 on the x-axis, 4.0 through 22.0 on the y-axis.  Include reasonable scale on each axis.  Graph the 2017 Sunrise data for Seattle then extend the graph one more year by drawing how you believe next year's graph will look.  EC: create a trigonometric function that will trace the graphs.
10/4 or 10/5
Define the words in simple terms and include a diagram
  • Amplitude.
  • Period.
  • Frequency.
Debrief 3 Oct homework--identify amplitude, period, vertical shift.

Complete and discuss the graph from the Can You Do The Can Can? activity.

Experiment with the Desmos Graphing Calculator to identify each coefficient does to the graph of y = sin(x) when we graph y = A sin B(x - C) + D.

JR:  Explain what each coefficient does to the graph of y = sin(x) when we graph y = A sin B(x - C) + D.  Include a few examples.
Graph the 2017 Sunset data for Seattle on the same axes as the homework from 3 October.  If your 3 October homework was performed incorrectly, fix it before proceeding.
10/6
How does creating a periodic function using y = A sin B(x - C) + D differ from using y = A sin (Bx - C) + D?
Getting Triggy activity: Determine each coefficient of y = A sin B(x - C) + D is necessary to create the graphs in both degrees and radians.

JR:  Explain, in detail, how to determine "B" to fit a set of periodic data with a sine function.
Create functions for both sunrise and sunset (Seattle, 2017) in both radians and degrees using y = A sin B(x - C) + D.  Remember to show how you determined each coefficient!!!!
10/9
Get ready for the quiz!  Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people. Quiz: modeling periodic data.  You may use a calculator and note card.

JR:  Under what conditions would the Law Of Cosines be used?  Give an example.
Copy and complete the table on the top of p. 417.
10/10 or 10/12
In a level, constant-speed turn the G-force on the airplane (and all inside) is related directly to the bank angle.  Copy the following table and model the data with a trigonometric function.

Debrief ET.

Investigate the graphs of sine, cosine, tangent, secant, cosecant, and cotangent.

Attempt Pushing The Envelope without a calculator.  When finished, check on a
calculator.
 
JR:  Explain why neither cosine nor cosecant are the inverse function for sine.  Include diagrams.
pp. 430-431 #85-86; p. 439 #62.
10/11
What do you want to know?
Homework debrief and other personal tasks.

JR:  Because of today's PSAT stealing most of the class there will be no formal JR.
Please confirm your sunrise and sunset models graph correctly and that you completed the Getting Triggy activity.

Consider investigating the Fun with Fourier activity as a way to model "square waves."
10/16
Construct the largest scale 3-4-5 triangle you can make in your homework notebook.  Measure the smallest angle (using a protractor).  Solve for the angle using trigonometry.  Are they "close?"
Construct an "inverse trig" table like Table 2 on p. 420 only having ratios for the top line for all six trig functions.  Hint, include values like 1, -1, 1/2, 31/2/2, etc.

JR:  Copy or paste the graph into your journal (hard copies available).   Give the graph an appropriate title and label the vertical and horizontal axes.  Explain the meaning of the graphs.  Attempt to write a general function that will trace all of the graphs if you use an additional variable, L, for the latitude.
pp. 444-445 #3-7.
10/17
Prepare to ask questions.  Consider using homework, quizzes, readings, etc. for sources.
In class review.

JR:  Explain the process of fitting a sine curve to data.
Prepare for the tests.
10/18 or 10/19
Get ready for the test!  Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people.  You may use calculator, ruler, protractor, compass. Test 5.1.  Trigonometry.  You may use a calculator and a non-mechanically reproduced 3 x 5 note card.  Expect questions on
  • Solving for unknown sides and angles of right triangles.
  • Modeling a periodic function from a Desmos graph.
JR: How did this test go for you?  Was there anything unexpected?  
Prepare for the next test.
10/20
Get ready for the test!  Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people. You may use calculator, ruler, protractor, compass. Test 5.2.  Trigonometry.  You may use a calculator and a non-mechanically reproduced 3 x 5 note card.  Expect questions on
  • Fitting a sine curve to real-world data.
JR: In what ways has your understanding of trigonometry improved over this unit?  Please be specific!  What understanding is still lacking?  
Complete the online Trigonometry Test.  Calculator allowed.  Note: this is NOT for a grade--it is a post-test of your understanding.  Do all problems in your homework notebook and record your score.

Before beginning the test, select "Multiple Choice Test," use 55 for "Seed Number," Trigonometry for "Select a Test," 20 for "How Many Problems?" then click "Take the test with problems chosen at random."  When finished, click "Submit Your Work and Get All The Problems Displayed."  Record your work and score in your homework notebook.
*Unless otherwise noted, homework is due the next class day.



Chapter 6: Trigonometric Functions: Right Triangle Approach
 Date

Entry Task

Activity

Assignment/Homework*

10/23
Explain the meaning of the trig functions depicted in the diagram.

Phred baked a pie that had a ten inch diameter and was cut into five equal slices.  Compute the area of each slice (sector) of pie.  Compute the length of crust for each sector of pie.

JR: Read the passage on Thales of Miletus (p. 486).  Explain in your own words what Thales contributed to the creation of trigonometry.
pp. 479-480 #73, 77, 79, 80.
10/24
What do you believe is the most common error on last week's Chapter 5 tests?  Give an example.
Discussion of Scaled Scoring.

Work in your table group to determine a set of suggestions to optimize assessment scores in Dr. Edge's class.  Agree upon a scribe (to record all comments), determine a natural order to suggestions based upon the comments (most important first), rewrite suggestions as directives (e.g. "get a good night's sleep before any assessment").  Prepare to present your suggestions to the class.

JR: Explain the "scaled scoring system" Dr. Edge uses on assessments (assume a ten point question).  
p. 481 #93, 94.  Include the graph (gluing in a printout is OK).
10/25 or 10/26
Compute the distance along a longitudinal arc on the surface of the earth that subtends a central angle of one minute (1/60 degree).  This distance is called a nautical mile (NM).  Note: the radius of the earth is about 3960 statute miles (SM). Comments on arc measure, particularly on the Earth's surface.

p. 489 #53-60.

JR: Explain how "angle of elevation" and "angle of depression" are used to solve real-world problems.  Give an example.
Finish the assigned problems and Copy the table at the bottom of p. 483.
10/27
Define "reference angle."  Hint: borrow a textbook and use the index to locate the term.
Copy and complete the tables from the Reference Angle activity into your homework notebook.

JR: Explain how a "reference angle" can be used to determine an unknown angle in a right triangle.
p. 500 #67, 68.
10/30
Read through the examples in Section 6.4 (pp. 501-506) with your table partners.  Determine what questions you still have regarding inverse trigonometric functions.
The Tripod activity.

JR: Explain the table for "The Inverse..." (p. 502) in simple language.  In what situations will the knowledge in this table be useful?
pp. 507-508 #44.
10/31
Complete p. 507 #43.
Complete p. 506 #5-8, checking answers with table groups AFTER you make an attempt.  Include sketches!

JR: Explain in simple language the meaning of tan-1(0.5) in simple language.  Include a diagram.
Catch up on all missing homework.  Make sure you include the date assigned, facts of the problems, and diagrams.
11/1 or 11/2
Trig Me activity.  You will receive a paper with the name of an inverse trig function on it.  Working alone, invent a problem that must use the function to solve.  Note: make it a problem, not an exercise!
Work selected invented problems in your homework notebook.

JR: Explain why there are two correct answers to .  Solve it!
p. 528 #28, 31.  EC for anyone correctly naming the airplane depicted in problem #32.
11/3
Get ready for the quiz!  Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people. Quiz: inverse trig.  You may use a non-mechanically reproduced note card,  ruler, and protractor on this quiz.  Calculator not allowed.

JR: Explain how to use a "unit circle diagram" to solve inverse trig problems.
Explain how trigonometry is used to determine the height of a mountain.  Include a sketch.  Reminder: you are guilty of plagiarism if you neglect to properly cite a source of information you present!!!
11/6
Solve p. 528 #32 using right triangle trigonometry.
Law of Sines (Section 6.5).

What We Can Do So Far activity.

JR: Explain why there is an "ambiguous case" for the Law of Sines.  What is the ambiguous case?
Finish the activity.
11/7 Work individually.  Create a triangle that results in an "ambiguous case" for the Law of Sines.  Solve for both possible triangles. Debrief ET and yesterday's activity.

Catch up on JRs and checking homework.

JR: Explain how to determine if the Law of Sines can be used on a given triangle.  Provide several examples.
p. 514 #29.

11/8 or 11/9
Define: course, heading, airspeed, ground speed, wind correction angle.
Law of Cosines (Section 6.6).

pp. 520-521 #5-10; 21-28.

JR: Explain how the Law of Cosines is related to the Pythagorean Theorem.  Give an example.
Finish the assigned problems.

11/13
Compute the area of the triangle that has side lengths 7.0 cm, 8.0 cm, and 9.0 cm.
Problem demonstrations by random selection.

p. 522 #39, 43, 45, 46, 48.

JR: Explain when to use which of the laws, Sines or Cosines.  Give several examples.
Finish the assigned problems.
11/14
Prepare to ask questions.
In class review: answering student-provided questions.

JR: Explain how to solve sin[cos-1(3/5)].  Include a diagram.
Prepare for the chapter tests.
11/15 or 11/16
Get ready for the test!  Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people.  You may use calculator, ruler, protractor, compass. Test 6.1: Trigonometry.  You may use a calculator and a non-mechanically reproduced 3 x 5 note card.  Expect questions on
  • Solving for unknown sides and angles of right triangles.
  • Solving for unknown sides and angles of non-right triangles.
  • Solving for central angles of circles, arc lengths, and sector areas.
  • Use angle measures that are in degrees or radians.
  • Use all the "big six" trigonometric functions.
  • Computing area of a non-right triangle given only the lengths of its sides or known angle and lengths of two sides.
JR: How well do you believe you were prepared for today's test?  Provide detail rather than generalities.
Prepare for the next test.
11/17
Get ready for the test!  Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people.  You may use ruler, protractor, compass. Test 6.2: Trigonometry.  You may NOT use a calculator or note card.  Expect questions on
  • Solving for unknown sides and angles of special right triangles.
  • Solving for central angles of circles, arc lengths, and sector areas.
  • Computing the result of composite trigonometric functions.
  • Computing area of a non-right triangle given only the lengths of its sides.
JR: Explain what you did to prepare for these chapter tests.  Provide detail rather than generalities.
Complete the online Trigonometry Test.  Calculator allowed.  Note: this is NOT for a grade--it is a post-test of your understanding.  Do all problems in your homework notebook and record your score.

Before beginning the test, select "Multiple Choice Test," use 211 for "Seed Number," Trigonometry for "Select a Test," 25 for "How Many Problems?" then click "Take the test with problems chosen at random."  Skip, omit, avoid, and otherwise do not answer the problems requiring identities (#11, 12, 14, 16, 25).

When finished, click "Submit Your Work and Get All The Problems Displayed."  Record your work and score in your homework notebook.
11/20
Get ready for the quiz!  Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people. Quiz: Geometry Terminology.  You may NOT use a calculator or note card.

JR: Explain how lengths and names are differentiated in geometry.  Give several examples.
Visit the CalcPrep Website and look under the Geometry tab.  Download the pdf under the second item (Challenging Pythagorean Theorem Problems).  Solve the first five problems in your homework notebook.
11/21
Continue working on the Challenging Pythagorean Theorem Problems downloaded yesterday. Finish the Challenging Pythagorean Theorem Problems.
 
JR: What do you know about vectors?  Provide examples.
None.  :-)
*Unless otherwise noted, homework is due the next class day.


Chapter 9: Vectors in Two and Three Dimensions
 Date

Entry Task

Activity

Assignment/Homework*

11/27
Define vector and scalar then classify each as either a vector or a scalar
  • Speed
  • Force
  • Debt
  • Velocity
  • Acceleration
  • Momentum
  • Energy
  • Temperature
  • Work
  • Friction
  • Current
Where Do They Point? activity.

JR: Explain why velocity is a vector and speed is not.
p. 637 #19, 20, 22 31.
11/28
Draw a more appropriate vector sum diagram for Example 6, p. 635.  Explain why yours is better than Figure 16.
A wind is blowing "N 30° E" (meaning the wind is flowing in the direction of 030°).  Compute North and East components of the wind if its speed is 55 mi/h.  Begin by drawing a diagram.

You are flying your HondaJet on a heading of 360° while encountering a 40 mi/h wind FROM 210° (going in the direction of 030°).  Make a scale diagram using 1 cm = 20 mi/h.  Solve for ground speed and course (measuring with ruler and protractor).  Recall that compass degrees begin by pointing "up" and increase clockwise.

JR: Explain HOW to determine the ground speed of an airplane if its airspeed is 120 mi/h and headed at 072° while it encounters a 22 mi/h wind from 180°.  Include a diagram.
p. 638 #53, 59, 63.
11/29 or 11/30
Below is an excerpt from NOAA's Aviation Weather Center "Winds Aloft Forecast."  Find the row for SEA and count over the third column of numbers.
GEG      2419-04 2614-10 3120-12
SEA 2214 2314-03 2524-06 2627-14
YKM 2005 2407-02 3013-06 2817-11
What it means: at 9000 feet in altitude (because of the third column) the winds are expected to be FROM 250° at 24 nautical miles per hour (abbreviated "24 KTS").  You may ignore the -06, because that is a temperature, in Celsius.

Use the wind information you found above and make a scale vector diagram for an airplane flying on a heading of 020° at 120 KTS.  Compute the ground speed by measuring the resultant vector.
Debrief ET, then determine what change must be made to the vector diagram so the airplane will remain flying 020° despite the wind.

Remember Law Of Sines.  Create a diagram and show how the law would be used.

Of Course activity.  Note: KBFI - KOMK: 125.0 NM; CRS 62° T.

JR: Explain how to determine heading, ground speed, and estimated time enroute for a flight when there are winds.
Determine wind correction angle (WCA), true heading (TH), ground speed (GS), and estimated time enroute (ETE) for a flight from Boeing Field (KBFI) to Yakima (KYKM).  The distance is 92.2 NM and the true course is 128°.  Choose a realistic airspeed and altitude.  Use NOAA's Aviation Weather Center "Winds Aloft Forecast" to get the Yakima winds.  Be sure to copy the facts into your homework notebook!
12/1
The following Winds Aloft are forecast for tomorrow morning.  At which location and altitude are the winds forecast to be strongest?  Explain.
GEG      2324-03 2425-09 2532-16 2543-28
SEA 2214 2420-05 2528-11 2538-18 2450-30
YKM 2510 2614-03 2422-09 2431-16 2553-27
Buddy up and create your own flight plan.  Consider "unusual" departure and destination points.  Choose a realistic airspeed and altitude.

JR: Explain how to determine estimated time of arrival (ETA).
Time to plan a trip to Disney Land!  :-)  You will depart from Boeing Field (KBFI) at noon Saturday and fly your Cirrus SR22 directly to John Wayne-Orange County Airport (KSNA).  The true course is 165° and distance 855 NM.  You expect an airspeed of 180 KTS at 18,000 feet and using San Francisco winds (2450-15) for planning.  Show all vectors and computations to compute your estimated time of arrival (ETA) at KSNA.
12/4
Write the equation of a circle that has a center at (2, -3) and the point (1, 1) is on the circle.
p. 675 #1, 2 (a & b), 3, 4, 8 (a & b).

JR: Explain how to create the equation of a sphere given the coordinates of its center and a point on the sphere.
Finish the problems.
12/5
Prepare to ask questions.
In class review.

JR: Explain how a "flight plan" combines both trigonometry and vectors.  Include a diagram.
Prepare for the tests.
12/6 or 12/7
Get ready for the test!  Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people.  You may use calculator, ruler, protractor, compass. Test 9.1: Vectors.  You may use a calculator and a non-mechanically reproduced 3 x 5 note card.  Consider also bringing ruler, protractor, and compass to use.  Expect questions on
  • Work in both degrees and radians.
  • Work with both basis vectors and those described in direction and length of vector.
  • Solving for sums of vectors graphically.
  • Solving for sums of vectors mathematically.
  • Solve scenario-based problems on force or velocity.
JR: Explain what you did to prepare for these chapter tests.  Provide detail rather than generalities.
Prepare for the next test.
12/8
Get ready for the test!  Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people.  You may use calculator, ruler, protractor, compass. Test 9.2: Vectors.  You may use a calculator and a non-mechanically reproduced 3 x 5 note card.  Consider also bringing ruler, protractor, and compass to use.  Expect questions on
  • Determine wind correction angle (WCA), true heading (TH), ground speed (GS), and estimated time enroute (ETE) for an hypothetical flight.
JR: In what ways has your understanding of vectors  improved over this unit?  Please be specific!  What understanding is still lacking? 
Watch THIS presentation on Dot Product.  Explain why the product is a scalar rather than a vector.
12/11
The length of vector u is 5.0 units and it points in the direction of 30.0°.  Determine the exact values for the components of u.
The Dot Product.  Address the following questions in your table group (write answers in your homework notebook)
  • How are the dot product of two vectors determined if you only know them by length and direction?  Include an example.
  • Why is uv = vu?  Include an example.
  • What does Dot Product actually mean?  Include a diagram.
JR: Given vectors a, b, and c.  Let a b = a c and a ≠ 0.  Must b = c?  Explain.
p. 646 #5, 6, 8, 9, 10.
12/12
What does "orthogonal" mean?  Include an example and diagram. Using the Dot Product to check for orthogonality, compute work, etc.

JR: Explain how "Dot Product" can be used to solve real-world problems.  Include an example you invented yourself.
p. 647 #46, 47, 50.
12/13 or 12/14
Explain how the game "Battleship" would work if played in 3-d.
Play Sky Wars.

JR: Explain a strategy for success in playing Sky Wars.
Draw the vector u = <3, 4, 5> making sure you show the vector <3, 4> in the x-y plane.  Compute | u |.  Hint: use the Pythagorean Theorem twice.
12/15
Get ready for the quiz!  Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people. Quiz: dot product.  You may use a calculator, note card, and drawing materials.

JR: "Invent" at least three "real-world problems" that require trigonometry to solve.  Be specific!
None.  :-)  Consider staying sharp by exploring and doing problems within the algebra, geometry, trigonometry, and functions areas.
*Unless otherwise noted, homework is due the next class day.


Chapter 8: Polar Coordinates and Parametric Equations
 Date

Entry Task

Activity

Assignment/Homework*

1/2
Name the highest peaks in Washington State, especially those visible from Seattle.  Include, if you can, the names indigenous people gave the peaks.
Peak My Interest activity.  Work in pairs and do all work in your homework notebook.  Make sketches for a "map view" (from overhead) of the peaks and villages along with separate "profile views" (from the side) to calculate heights of peaks.

JR: The "GPS Coordinates" (latitude and longitude) of Boeing Field/King County International Airport (BFI) and  Spokane International Airport (GEG) are, respectively, N 47° 31.80', W 122° 18.12'; N 47° 37.14', W 117° 32.11'.  Compute the distance between the airports using their latitude and longitude.
p. 530 #81, 82, 84.
1/3 or 1/4
Explain how the polar coordinate (3, 30°) would be graphed.  Include a diagram.
Play two games of Polar Tic-Tac-Toe.

JR: Explain how to convert a polar coordinate, such as (3, 30°), into Cartesian coordinates.
Graph the sun transit data for Boston and Seattle on polar azimuth graph paper.  Make Boston's marks in a different pigment than Seattle's!  Note the polar graph is set up like a compass where you will mark (Altitude, Azimuth) as (r, theta).  The time will not be graphed.

Explain the similarities and differences between the plots in your homework notebook.
1/5
Give the radian equivalent to these angle measures
  • 30°
  • 45°
  • 60°
  • 90°
  • 120°
  • 240°
  • 300°
Uniqueness of Representation activity.  Write prompt and answer in homework notebook.  Note: the angles in problem 2 are in radians.

JR: Explain how to convert a Cartesian coordinate, such as (-3, 4), into  polar coordinates.
Complete Some Basic Polar Graphs in your homework notebook.  Remember to explain what the graph is representing, list the points you are graphing, etc.
1/8
Express the equation x2 = 4y in polar coordinates.
Discuss the conversion examples on p. 591.

Create a diagram where a polar graph is overlaid on a Cartesian graph.  Use the graph to explain the conversion of (3, 4) and (2, 60°) to the other system

JR: Explain why the x-coordinate for (r, theta) is r•cos(theta).  Include a diagram.
Finish the polar/Cartesian graph begun in class.  Include two points of your choosing, one in QII and the other in QIII.
1/9
Determine the Cartesian coordinates of (2, 3π/4).  Use both trigonometry and your polar/Cartesian graph from yesterday. More converting between polar and Cartesian.  Challenge a partner: give a coordinate for your partner to convert--both give a polar to convert, then both give a Cartesian.

JR: Explain the process of converting between polar and Cartesian coordinates.
p. 593 #45, 46, 47, 51, 54, 61.
1/10 or 1/11
Graph r = 4cos(2theta) using 0 ≤ theta ≤ 360; theta step = 5; Xmin = -6; Xmax = 6; Ymin = -4; Ymax = 4.  What did you get? Graphs of polar equations.  Cardioids activity.

Discuss the examples in Section 8.2 (pp. 594 - 599).
 
JR: Explain how the example polar equations are functions even though they violate the "vertical line rule" you were previously taught.  Include diagrams.
p. 600 #32, 39, 41.  Graph "test points" then connect rather than copying the graph from a device.

Consider using printing, cutting out, and pasting the polar graph axes into your homework notebook for the sketches.  Remember to label the graphs!!!
1/12
Look through the section on parametric equations (Section 8.4, pp. 611-616) to determine how they would make modeling the motion of a projectile (e.g. the flight of a ball) easier. Introduction to parametric equations.

It's About Time activity.

JR: Explain the purpose of the "parameter" in parametric equations.
Graph the functions within the following problems by creating and using tables, like with today's activity.  You do not need to follow the book's instructions for the problems.  Note: the angle measures will be in radians.
p. 617 #3, 5, 13, 14.
1/16
Provide the value, including units, for the following
  • the acceleration due to gravity in SI.
  • the acceleration due to gravity in SAE.
  • the distance an object moves in four seconds if it is traveling 25 m/s.
  • the distance an object moves in T seconds if it is traveling 25 m/s.
A projectile is launched at a 40° angle.  Explain in simple language how the horizontal component of the projectile's velocity changes over the projectile's flight if its speed is low enough for air resistance to be negligible.  Include diagrams.
 
JR: Explain why d = 1/2 at2 for uniform acceleration.
Write parametric equations for a golf ball struck at 101 ft/s with a club angle of 22 degrees.  Determine how far, horizontally, will the ball travel.
1/17 or 1/18
Phred is golfing and finds himself “stymied” in the woods.  He is 25 yards away from a 50 feet tall tree and 95 yards away from the center of the green.  He selects a club with a 42° loft and will use a swing that results in a 106 feet per second club-head speed.  Note: 1 yard = 3 feet.  Analyze the outcome of Phred’s shot.
On the next hole, Phred is 25 yards away from a 65 feet tall tree and 95 yards away from the center of the green.  He selects a club with a 55° loft and will use a swing that results in an 89 ft/s club-head speed.  Analyze the outcome of Phred’s shot.

Problem demonstrations in preparation for Friday's test.

JR: Explain the process of converting between parametric and Cartesian coordinates.
Prepare for Friday's test.
1/19
Get ready for the test!  Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people.  You may use calculator, ruler, protractor, compass. Test 8.1: Polar and Parametric Equations.  You may use a calculator and a non-mechanically reproduced 3 x 5 note card.  Consider also bringing ruler, protractor, and compass to use.  Expect questions on
  • convert coordinates between polar and Cartesian.
  • convert coordinates between parametric and Cartesian.
  • create simple polar or parametric graphs.
  • create parametric equations for a scenario.
JR: Explain some practical uses of polar and parametric equations.  Be specific and include diagrams.
Review previous activities, homework, quizzes, and tests and bring questions on any concept you are still uncertain.  Prepare for Monday's study session.
*Unless otherwise noted, homework is due the next class day.


Semester Final: Preparation and Administration
 Date

Entry Task

Activity

Assignment/Homework*

1/22
Prepare to ask questions.
Demonstration and/or explanation of student-provided examples and problems.

JR: Explain
Prepare for the next study session.
1/23
Prepare to ask questions. Demonstration and/or explanation of student-provided examples and problems.

JR: Explain
Prepare for the Final Exams.
1/24 or 1/25
Get ready for the exam!  Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people.  You may use calculator, ruler, protractor, compass. Final 1.1.  You may use a calculator and a non-mechanically reproduced 3 x 5 note card.  Consider also bringing ruler, protractor, compass, and extra cells for your calculator.  Expect questions on
  • Solving for unknown sides and angles of right triangles.
  • Solving for unknown sides and angles of non-right triangles.
  • Modeling a periodic function from a Desmos graph.
  • Solving for central angles of circles, arc lengths, and sector areas.
  • Computing area of a non-right triangle given only the lengths of its sides or known angle and lengths of two sides.
  • Vector arithmetic, including dot product.
  • Graph points from a given polar function.
  • Create parametric functions for a scenario.
You should be able to
  • Use angle measures that are in degrees or radians.
  • Use all the "big six" trigonometric functions.
JR: Explain
Prepare for the next Exam.
1/26
Get ready for the exam!  Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people.  You may use calculator, ruler, protractor, compass. Final 1.2.  You may use a calculator and a non-mechanically reproduced 3 x 5 note card.  Consider also bringing ruler, protractor, compass, and extra cells for your calculator.  Expect a question on
  • Determine wind correction angle (WCA), true heading (TH), ground speed (GS), and estimated time enroute (ETE) for an hypothetical flight.
JR: Explain

*Unless otherwise noted, homework is due the next class day.



Semester Mini-Project
 Date

Entry Task

Activity

Assignment/Homework*

1/29



1/30



1/31 or 2/1





Click here for the Reference Pages from Stewart Calculus (7th Edition).

Create and print your own graph paper at THIS Website.

Below are various documents on the operation of the class

Course syllabus

Also note the additional items

    Email: richard.edgerton@highlineschools.org