Test Review Questions - Chapter 2 - Periodic Functions and Right Triangle Problems

Periodic Functions and Right Triangle Problems:

Questions--Chapter Review pp. 78-80

R0. Update your journal with what you have learned since the last entry. Include sucn things as
How angles can have measures that are negative or greater than 180? and reference angles.
The definitions of sine, cosine, tangent, cot, secant and cosecant.
Why sine and cosine graphs are periodic
Inverse trigonometric functions used to find angles
Applications to right triangle problems

R1. Hose Reel Problem: You unwind a hose by turning the crank on a hose reel mounted to the wall (Figure 2-6a) . As you crank, the distance your hand is above the ground is a periodic function of the angle through which the reel has rotated (Figure 2.6b, solid graph). The distance, y, is measured in feet, and the angle theta, is measured in degrees.

a. The dashed graph in Figure 2-6b is the pre-image function y = sin theta. Plot this sine function graph on your grapher. Does the result agree with Figure 2-6b?

b. The solid graph in Figure 2-6b is a dilation and translation of y = sin theta . Figure out what the two transformations are, and write an equation for the function. When you plot the transformed graph on your grapher, does the result agree with Figure 2-6B?

c. What is the name for the periodic graphs in Figure 2-6b?


R23. For each angle measure, sketch an angle in standard position. Mark the reference angle and find its measure.
a.
b.
c.

R3.

a. Find sin theta and cos theta given that the terminal side of theta contains the point (u,v) =
(-5,7).
b. Find decimal approximations for sin 160 degrees and cos 160 degrees. Draw a 160 angle in standard position in a uv-coordinate system and mark the reference angle. Explain why sin 160 is a positive but cos 160 is negative.

c. Sketch the graphs of the parent sinusoids y = cos theta and y = sin theta.
d. In which two quadrants on a uv-coordinate system in sin theta negative?
e. For y = 4 + cos 2 theta, what are the transformations of the parent function graph y = cos theta? Sketch the graph of the transformed function.


R4. Find a decimal approximation fo rcss 256.
b. Find exact values (no decimals_) of the six trig functions of 150 degrees.
c. Find the exact values of sec theta is theta ref = 45 and theta terminates in Quadrant III.
d. Find the exact value of cos theta if the terminal side of theta contains the point (-3,5).
e. Find the exact value of sec (-120 degrees).
f. Find the exact value of tan 2 30 degrees - csc 2 30 degres.
g. Explain why tan 90 is undefined.

R5. a. Find a decimal approximation for theta = cos -1 0.6 . What does the answer mean?
b. Galleon Problem: Imagine that you are on a salvage ship in the Gulf of Mexico. Your sonar system has located a sunken Spanish galleon at a slant distance of 683 m from your ship, with an angle of depression of 28 degrees.

i. How deep is the water at the location of the galleon?
ii. How far must your ship go to be directly above the galleon?
iii. Your ship moves horizontally toward the galleon. After 520 m. what is the angle of depression?
iv. How could the crew of a fishing vessel use the techniques of this problem while searching for schools of fish?








Questions--Chapter Review pp. 125-128




Questions--Chapter Review pp. 166-168


Questions--Chapter Review pp. 256-260