Math 12 – Precalculus – fall ’04 – Chapter 5 Test         Name_________________________

Write all responses on separate paper. Show all the work for credit. Do not abuse a calculator.

1.      Suppose a terminal point determined by t is the point . 

a.       Verify that the point lies on the unit circle.

b.      What are the coordinates of the terminal point for ?

c.       What are the coordinates of the terminal point for ?

2.      Suppose a terminal point determined by t is P(x,y) on the unit circle, where . 

a.       What quadrants could P be in?

b.      What are the absolute values of the coordinates of x and y ?

c.       Find exact representations for the values of  csc(t) and cot(t).

3.      Suppose a terminal point P(x,y) in QIV on the unit circle has y-coordinate . Find

a.      

b.     

4.      Find the reference number for each and plot its position on the unit circle together with exact values (in simplest radical form) for the x and y coordinates of the point.

a.     

b.     

5.      Suppose that .  Estimate the corresponding intervals for the values of  cos(t) and sin(t) and highlight these on the diagram at right: 6.      Find the amplitude, period and phase shift of the  and sketch a graph showing at least one wave form.  Be careful scale and label axes in your graph. 7.      Find the period and at least two asymptotes and graph the function  .

 

8.      Find sinusoidal formula which fits the graph shown below: