Lab06
Name:
Start time: border="0" Number of questions: 12
This set of questions goes with the pages of applets and activities for Lab 06.  Use the applets and activities there to answer the questions.
 

Question 1  (1 point)
Refer to lab page 2. Let angle CAD be represented as . What is angle C'A'D' ?

 


Question 2  (1 point)
Refer to lab page 2. Match the cyan, magenta,
yellow, and green
lines with the appropriate trig functions.

1. cyan   a. sin 2
2. magenta   b. sin
3. yellow   c. cos 2
4. green   d. cos

 


Question 3  (1 point)
Refer to lab page 2. Hit the Revolve D button and note what happens.

 


Question 4  (1 point)
Refer to lab page 2. What is the period of the function y=cos(2x) ?

 


Question 5  (1 point)
Refer to lab page 3. Use the utility to graph cos(2x). Now zoom in to find the x coordinate of the smallest positive x intercept. Answer accurate to three decimal places.


 


Question 6  (1 point)
Refer to lab page 3. Refresh the grapher's display and plot cos(x)2 (the syntax for the grapher is cos(x)^2). What is the period of cos(x)2 ?

 


Question 7  (1 point)
Refer to lab page 3. Now plot cos(x)2 - sin(x)2 in the other color. What fact about the graph supports the fact that cos(2x) = cos(x)2 - sin(x)2 is a trig identity?

 


Question 8  (.5 points)
Use the grapher on page 3. What right hand side f(x) makes (cos x)2 (1 + (tan x)2) = f(x) an identity?

 


Question 9  (.5 points)
Use the grapher on page 3. What right hand side f(x) makes sin( /2 + x) = f(x) an identity?

 


Question 10  (.5 points)
Use the grapher on page 3. What right hand side f(x) makes 1 - (cos x) 2 /(1 + sin x) = f(x) an identity?

 


Question 11  (.5 points)
Use the grapher on page 3. What right hand side f(x) makes (cos x)4- (sin x)4 = f(x) an identity?

 


Question 12  (1 point)
Use the grapher on page 3. For a between -10 and 10 there are three values of a in the list below for which sin x = cos (x - a). What are they?