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TRIGONOMETRY REVIEW

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.
2. On a unit circle, mark and label the points determined by
 
,
6 3
,
5
11
, and
2
4
3. Sketch a graph of y  cos x
4. What is the range of cosine function?
5. What is the period of the sine function?
6. What is the domain of the sine function?
7. What is the amplitude of the cosine function?
8. Complete the following table:
x

3
7
4

3
2
sin x
cos x
9. Sketch a graph of the tangent function.
10. What is the period of the tangent function?
11. What is the domain of the tangent function?
12. What is the range of the tangent function?
13. In which quadrants are the signs of the tangent and cosecant alike?
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
15. Convert to degree measure:
9
a)
4
b) 3 radians
16. Find the length of an arc of a circle, given a central angle of
5
and a radius of 8
6
centimeters.
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.?
18. Find the six trigonometric function values for the angle  shown:
-6

-5
19. Find the following exactly:
a) tan 480 o
b) sin( 120 o )
c) cos( 240 o )
1
and that the terminal side is in quadrant II, find the other five
3
trigonometric function values.
20. Given that sin  
21. Convert 28.35 o to degrees and minutes
22. Convert 89 o 36 to degrees.
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 )
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
25. Use a calculator to find  in the interval indicated:
a) sin   0.5932, (90 o ,180 o )
b) tan   5.321,
 
( , )
2 2
26. Sketch the graph of y  2 sin( x   ) .
27. What is the period of the function in Question 26?
28. What is the phase shift of the function in Question 26?
1
29. A point on the unit circle has an x-coordinate of  . What is the y-coordinate?
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