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TRIGONOMETRY REVIEW ANSWERS

5 2
,  is on a unit circle. Find the coordinates of its reflection across
1. The point  
3
3

the origin, the x-axis, and the y-axis.
Answer:
 5 2

 5 2
5 2
,  ; the x-axis:  
, 
the origin: 
,  ; the y-axis: 
3
3
3
3
3
3





  5
11
, and
2. On a unit circle, mark and label the points determined by , ,
6 3
2
4
Answer:
3. Sketch a graph of y  cos x
Answer:
4. What is the range of cosine function?
Answer: [-1, 1]
5. What is the period of the sine function?
Answer: 2
6. What is the domain of the sine function?
Answer: all reals
7. What is the amplitude of the cosine function?
Answer: 1
8. Complete the following table:
Answer:
x
sin x
cos x

3
3
2
1
2
7
4

2
2
2
2

3
2
1
0
9. Sketch a graph of the tangent function.
Answer:
10. What is the period of the tangent function?
Answer: 
11. What is the domain of the tangent function?

Answer: all reals except x   n
2
12. What is the range of the tangent function?
Answer: all reals
13. In which quadrants are the signs of the tangent and cosecant alike?
Answer: I and IV
14. For the angles of the following measures, state in which quadrant the terminal side
lies, and convert to radian measure in terms of  :
a)  210 o
b) 54 o
c) 225 o
Answer:
7
a) II, 
6
3
b) I,
10
5
c) III,
4
15. Convert to degree measure:
9
a)
4
b) 3 radians
Answer:
a) 405 o
b) 171.89 o
5
16. Find the length of an arc of a circle, given a central angle of
and a radius of 8
6
centimeters.
Answer: 20.94 cms
17. A wheel with a 14-cm diameter is rotating at a speed of 10 revolutions per second.
What is the velocity, in cm/sec of a point on the rim.?
Answer: 440 cms/sec
18. Find the six trigonometric function values for the angle  shown:

-6
-5
Answer:
sin   
5
61
, cos  
6
61
, tan  
61
61
5
6
, csc   
, sec   
, cot  
6
5
5
6
19. Find the following exactly:
a) tan 480 o
b) sin( 120 o )
c) cos( 240 o )
Answer:
a)  3
3
2
1
c) 
2
b) 
1
and that the terminal side is in quadrant II, find the other five
3
trigonometric function values.
Answer:
2 2
3
3 2
cos   
, tan   
, csc  3 , sec  
, cot   2 2
3
4
4
20. Given that sin  
21. Convert 28.35 o to degrees and minutes
Answer: 28 o 21 ,
22. Convert 89 o 36 to degrees.
Answer: 89.6 o
23. Use a calculator to find each of the following:
a) sin( 153o 15 17 )
b) cos(1.115)
17
)
c) tan( 
3
d) sec(19 o 15 )
e) csc(3.5124)
f) cot(1573o )
Answer:
a) –0.450025
b) 0.440177
c) 1.73205
d) 1.05922
e) –2.75963
f) –0.932515
24. Use a calculator to find the acute angle  that is a solution of the equation. Give the
answer in radians:
a) cos  0.5324
b) csc  2.1538
Answer:
a) 1.0094
b) 0.4828
25. Use a calculator to find  in the interval indicated:
a) sin   0.5932, (90 o ,180 o )
b) tan   5.321,
 
( , )
2 2
Answer:
a) 143.62 degrees
b) –1.3850 radians
26. Sketch the graph of y  2 sin( x   ) .
Answer:
27. What is the period of the function in Question 26?
Answer: 2
28. What is the phase shift of the function in Question 26?
Answer:  
1
29. A point on the unit circle has an x-coordinate of  . What is the y-coordinate?
4
15
Answer: 
4
30. Solve the following equations, if possible:
a) 8 cos x  10
b) 2 sin 2   sin   1
c) tan 2   5 tan   3  0
Answer:
a) No solution
 7 11
,
,
b)
2 6 6
c) 1.7992, 2.5327, 4.9407