UNIT 7  :  TRIGONOMETRIC FUNCTIONS

 LESSON 8 :  TRIGONOMETRIC FUNCTIONS TEST & SOLUTIONS

 

 

1.  Convert each of the following to degree measure.

 

3.  An electric motor turns at 3600 rpm’s (rev’s per minute).  Express this angular velocity in radians per second to the nearest hundredth.

 

5.  Find the exact value of the following.

  

 

6.  Sketch the graph of the basic function   Use transformations to sketch  .

     Find the amplitude, period, phase shift, domain and range.

 

7.  The graph below shows a sine function of the form  y = a sin k(x – d) + c.  find the values of the parameters a,k, d, c.

 

 

 

9.  Prove the following identities.

 

 

 

 

 

 

Solutions:

 

1.  Convert each of the following to degree measure.

 

 

 

 

 

 

 

 

.

     Find the amplitude, period, phase shift, domain and range.

 

 

x0	0	90	180	270	360
y	1	0	-1	0	1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

In radians, the points (see table at top of page) would be:

 

Amplitude:   |a| = ½

Domain of 1 period or cycle (between red dots on graph):

Range: The maximum value of y is -0.5 and the minimum value is –1.5

 

 

 

7.  The graph below shows a sine function of the form  y = a sin k(x – d) + c.  find the values of the parameters a,k, d, c.

 

    

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

9.  Prove the following identities.

 

Proof:

 

 

 

Proof:

 

 

 

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