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Name: _____Answer Key______
ACM3
Trig Basics Review Key
~Make sure that you know the unit circle and that you can evaluate the trig functions of any
value on it:
 5 
 4   3
 17  2 3
 9 
1. sec 
2. cot 
3. csc 
4. tan 
= 2
=
=
 = -1
3
3
 3 
 3 
 3 
 4 
~You must also use the unit circle to solve equations for all values 0    2 :
 3
csc   2
cot   1
tan   3
sin  
2
5.
6.  4
7.  5
8. 3 7
,
,
4 5
,
,
6 6
4 4
3 3
3 3
~When you are given a value not on the unit circle, you must use your calculator:
 3 
 15 
9. cot 
10. sec 
 =1.5270
 =2.0765
 11 
 7 
 19 
11. sin  32 15'45" =0.5338
12. csc 
 =1.7013
 5 
~ Evaluate the following inverse trig functions to find the radian measure of the angle:
13. sin 1 .3428 = .3499
14. cos1 .2876  = 1.2791
1


15. cot 1  24.3827   tan 1 
  .0410
 24.3827 
 1 
16. sec1  4.8176   cos 1 
  1.3617
 4.8176 
~You have to know where particular trig functions are positive and negative:
17. Is sin  positive or negative in quadrant IV? negative
18. Which quadrant are you in if csc  0 and tan   0 ? III
~You must be able to find a positive coterminal and a negative coterminal angle, graph the angle
in standard form and state the reference angle:
19. Given the angle 36 , find all of the above mentioned information:
Coterminals: 396 324
Reference Angle: 36
Standard position: terminal side is in quadrant one and the angle is measured
counterclockwise
ACM3
Trig Basics Review Key
5
20. Given the angle
, find all of the above mentioned information:
11
27 17
5
Coterminals:
Reference Angle:
11
11
11
Standard position: terminal side is in quadrant one and the angle is measured
counterclockwise
21. Change #23 to a radian and #24 to a degree

and 81.8182
5
22. Convert 67.9362o to Degrees, Minutes, Seconds 67 56 '10.32"
23. Convert 45 26 '38" to Decimal Degrees 45.4439
~You must be able to find the EXACT VALUE of any trig function given particular pieces of
information:
24. Given that the terminal side of  lies on the line y=-3x in quadrant II, find the value of
10
csc  
3
2
25. Given that cot  
and sec  0 , find tan   
7
7
tan     *Since theta is in quadrant IV, negative theta is in quadrant I
2
26. Given the point (-4, -6) on the terminal side of  , find the value of cos (or any of the
2 13
other six trig functions) cos  
13
~You must know right triangle trig and how to use it to solve various word problems:
27. A guy wire stretches from the top of an antenna tower to a point on level ground 18 feet
from the base of the tower. The angle between the wire and the ground is 63 . How high is the
tower? 3.0555ft
28. A plan takes off at an angle of 6 traveling at the rate of 200 feet/second. If it continues
on this flight path at the same speed, how many minutes will it take to reach an altitude of
8000 feet? 6.3778 min
29. A rocket shoots straight up from the launch pad. Five seconds after lift-off an observer 2
miles away notes that the rocket’s angle of elevation is 3.5 . Four seconds later the angle of
elevation is 41 . How far did the rocket rise during those 4 seconds? 1.6163 miles