CHAPTER 8 TEST (8.1 – 8.4)
You Should Be Able To:
 Find the complement, supplement of an angle
 Sketch an angle in standard position
 Find coterminal angles
 Change between degrees and radians
 Find the length of an arc and the area of a sector (angle in radians!)
 Change between decimal degrees and degrees, minutes and seconds
 Add and subtract degrees and minutes
 Find the quadrant or axis of the terminal side of an angle
 Find the angular or linear speed
 Find the six trig functions for an angle given a point on the terminal side
 Use the unit circle to find the exact sin, cos, tan, csc, sec, or cot of special angles
 Find the amplitude, period, phase shift, vertical translation and range of a trig
function
 Graph all six trig functions
 Write the equation of sin or cos from a graph or given info
REVIEW PROBLEMS
If angles are given in radians, answers should be in radians (same with degrees).
5
1. Find the complement of 26°39'.
2. Find the supplement of
6
3. Sketch the given angle in standard position.
a. -220°
b.
11
8
4. Find the angle of smallest possible positive measure coterminal with an angle of the
given measure. Also, find the quadrant or axis of the terminal side.
3
a. -276°
b.
2
5. Convert degrees to radians and radians to degrees.
6
a. 800°
b.
5
6. The length of the minute hand of a clock is 3 inches. If it has moved 135°, find the
length of the arc and the area of the sector formed. (s = rθ and A = ½r²θ).
7. Change to decimal degrees to the
nearest thousandth.
41°52'29"
8. Change to degrees, minutes, seconds to
the nearest second.
87.392°
9. Find the six trigonometric functions for θ in standard position whose terminal ray
passes through (7, -24).
10. Determine what quadrant each angle is in if θ is an angle in the unit circle:
a. sin θ > 0 , cos θ < 0
b. sin θ < 0, tan θ > 0
11. Earth revolves on its axis once every 24 hours. Assuming that Earth’s radius is 6400
km, find the following:
a. Angular speed of Earth in radians per day
b. Linear speed at the North Pole or South Pole
c. Linear speed at Quito, Ecuador, a city on the equator
NO CALCULATOR FOR THE FOLLOWING PROBLEMS!!
Use the unit circle to evaluate each exactly.
12. sin (-60°)
13. csc (240°)
14. tan (480°)
15. cot (315°)
16. sec
5
4
 
17. cos   
 3
18. sin
4
3
19. tan
13
6
Give the (a) amplitude, (b) period, (c) phase shift, (d) vertical translation, and (e) range
for each of the following.

 x

20. y  2 sin    1
21. y  3 sec 2 x  
4
4

22. y  4 tan( 3x)  2


23. y  cos 4 x    3
2

Write the equation of a sine or cosine function having the given graph.
24. sine
25. cosine
Graph two periods of each of the following functions.


26. y  2 sin  2 x  
2

27. y  2 cos3x  1


28. y  sec x  
4

29. y = 4 tan x