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 PreCalculus
Date 
Entry Task 
Activity 
Assignment/Homework* 
9/17 
Compare objects and processes used in last
night's homework at your 4top. A spokesperson for
your group will compile a list of commonalities and
explain to the class when it is your group's turn to
speak. 
Begin to make a Trigulator. JR: Use simple language to explain the meaning of "the unit circle" (a trigonometric term). 
Finish the Trigulator II. 
9/19 
List the three ratios from Trigulator II along with their largest and smallest values.  Use your results from Trigulator II to set
up and solve the following problems

Finish the problems begun in class. 
9/22 
Explain how to solve for the measure of one
of the acute angles of a right triangle if you know the
lengths of two legs AND are using the table from
Trigulator II. 
Debrief the homework. Begin Trigulator III. JR: Explain how you would improve Trigulator I and Trigulator II so you would get "more accurate" results when computing the measures of unknown parts of triangles. 
Finish Trigulator III. 
9/23 
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: use ratios from YOUR Trigulator
II to set up equations that will solve for an
unknown side or angle of a triangle. No calculator
or notes. No accommodations will be made for those
who do not have their Trigulator II completed or
with them. JR: Explain how to determine the height of a structure indirectly (i.e. by using trigonometry). 

9/24 
YOUR ruler and protractor
are required for this! Create a scale diagram (use ruler and protractor) that satisfies the following conditions

Use your diagram from the
ET to determine the height of the object that casts the 55
m shadow. Construction of a "clinometer" from a protractor. How to make one is available from the Exploratorium or you can use THIS file from NCTM. JR: Explain in simple language how to modify and use a protractor to determine angle of elevation and angle of depression. 
Use your clinometer (made
from a protractor) to measure the

9/26 
List several applications
of trigonometry. 
Try Angles
activity. JR: If the lengths of the sides of a triangle are a and b, write an expression for the maximum and minimum lengths of the third side. 
Finish Try Angles. 
9/29 
Which trigonometric
functions are associated with the last two columns of the
Try Angles
activity? Explain the significance of the ratios in
relation to the measure of angle B. 
Debrief Try Angles. Issue textbooks. Begin Textbook Scavenger Hunt. Write answers into your homework notebook. JR: List some ways to protect and preserve your textbook. 
Finish Textbook Scavenger Hunt.
Write answers in your homework notebook. 
9/30 
Sketch the situation from
p. 313 #6. 
Do Lesson 5.1 (Right
Triangles) pp. 303310. See THIS graphic for the relationship between degrees and radians along with quadrant positivity for each trig function. JR: List what must be included on every assignment problem to receive credit. 
Pg. 311 #1, 2, 3. 
10/1 
Construct a right triangle having legs 6.0 cm and 8.0 cm. Measure the angles and hypotenuse. Explain how "inverse trig functions" will solve for the angle measures.  Inverses.
Lesson 5.2 (pp. 318324). Write a summary in your homework notebook: explain the relationship between a trig function and its resultant ratiodiscuss from the standpoint of the function and "movement" on your "Trigulator III" paper. JR: Explain, in detail, the purpose of an "inverse function." Give several examples (both trigonometric and nontrigonometric). 
Pgs. 325326 #3, 5. Click the links to see a 35 mm camera and 35 mm film (from which negatives are made). 
10/3 
Explain how similarity of
triangles is related to trigonometry. 
The Sims
activity. JR: Explain how to use similarity of triangles to solve for unknown parts of a triangle. 
Use known ratios from the
triangles you created in The Sims
activity to solve for the unknown parts of the given
mystery triangles. DO NOT solve by scale drawing or
using trigonometry. Write ratios from the known
triangles and solve the proportion using algebra.
Use only the arithmetic functions from your calculator (+,
—, x , ÷). Begin each problem with a sketch of the
mystery triangle and include a sketch of the corresponding
known triangle (from the first page of this activity).

10/6 
p. 325 #1. 
Quiz 5.1
(trigonometry). You may use YOUR calculator and a 3
x 5 note card** (writing on both sides is
permitted). Measurement devices (e.g. YOUR ruler and
protractor) are also allowed. **Note cards may not be mechanically reproduced (no photo copies, word processing, etc.). JR: Explain in simple language how to solve for unknown sides and angles of a right triangle given: a) two sides are known; and, b) one angle and the side opposite the angle are known. 
Pg. 327 #7, 8. 
10/7 
The height of a mountain
(relative to its surroundings) can be calculated by
finding the angle of elevation to the peak, moving away
from the mountain a measured distance, and finding the new
angle of elevation. Draw the situation, “invent”
some measures, and solve for the height of the mountain. 
Oblique triangles:
Lesson 5.3 (Pgs. 329335). Additional notes on
the laws of Sines and Cosines is HERE. JR: Explain when to use the Law of Sines rather than the Law of Cosines. 
Pgs. 336338 #1, 3. 
10/8 
Draw an arbitrary triangle
ABC and measure the sides and angles. Confirm the
Law of Sines for all three angle/side ratios. Check
to see if the ratio of cosines are also equal (i.e. cosine
(A)/a = cosine (B)/b). Write a conclusion of your
observation. 
Work with table partners onThe Law of Sinesand The Law of Cosines.JR: A baseball "diamond" is comprised of a home plate along with first, second, and third basesall ninety feet away from the previous base. The pitcher must throw from a "rubber" that is 60 feet and 6 inches (that is, 60.5 feet) from home plate. How far is the pitcher's rubber from first base? Include a diagram! 
Pgs. 340342 #9, 13. 
10/13 
Make a sketch and solve for
the unknown side for triangle ABC

Pgs. 338339 #4, 5. JR: Draw equilateral triangle ABC. Does a^{2} + b^{2} = c^{2}? Why/why not? Speculate how this problem relates to other triangles. 
Pg. 339 #6; p. 341 #11. 
10/14 
The shadow of one of Blair's Cuspids was approximately 110 meters when the Sun was at an angle of elevation of 10.9 degrees. Compute the height of the cuspid if the ground were level, if the ground sloped downward at 5.0 degrees and if the ground sloped upward at 5.0 degrees.  Begin working on the Chapter 5 Review (Pgs.
343344 #110). JR: Under what conditions would it be impossible to solve for the unknowns of a triangle even though you know three facts (at least one of which is a side)? Create a scale drawing. 
Finish the Chapter 5 Review. For #7, assume the towers are on the same line of latitude. 
10/17 
List the domain and range for each of the
following functions

Peak My
Interest activity. JR: Why must the distances between the two mountains in today's activity be computed using Law of Cosines rather than using proportions from the distances between villages B and C? 
Finish today's activity. Recommended problems: Pgs. 327328 #9, 12, 13. Note: on "concavity:" While concavity is defined more formally, loosely, we can think of concave up as a part of a function with a smile or curves upward. Concave down is a function which frowns or curves downward (courtesy Mr. G). See also 
10/20 
Weather balloons provide soundings that give a profile of the atmospheric conditions. Before GPS wind speed and direction were calculated by measuring altitude and downrange movement. Explain how the math for this works.  Inclass review.
Bring questions & concerns! JR: Under what circumstances will the Law of Cosines give the wrong answer? Explain why. 
Prepare for the test. Consider beginning the Chapter 5 Takehome. Note: the downloadable version is in color with a larger diagram on page 2. :) 
10/21 
Get ready for the test! Move to a seat where you have ample room, obtain all the materials you need before class starts, put yourself in a positive mental state.  Test 5.1. You
may use YOUR calculator and a 3 x 5 note card** (writing
on both sides is permitted). Measurement devices
(e.g. ruler and protractor) are also allowed, however they
can only be the ones you brought to class. Expect
questions on
JR: What were the hardest parts of Chapter 5 for you? What were the easiest parts? 
Prepare for the
test. Consider continuing the Chapter 5 Takehome. 
10/23 
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.  Test 5.2. You may use a 3 x 5
note card* (writing on both sides is permitted).
Measurement devices (e.g. ruler and protractor) are
required, however, they may only be the ones you brought
to class. Calculator NOT allowed. Expect a
problem on determining a trigonometric value using a scale
diagram. **Note cards may not be mechanically reproduced (no photo copies, word processing, etc.). JR: Suggest some ways Dr. Edge's teaching of this unit could be improved. 
Finish the Chapter 5 Takehome. 
10/24 
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. Have your homework notebook ready and computer activated. Note: today is the last day any late papers will be scored this quarter! 
Trigonometry posttest. Calculator
allowed. Note: today is the last day any late papers will be scored this quarter! JR: Did you improve versus the pretest on this unit? If so, why? If not, why not? 
Explain each of the following
