Name_______________________________________
Date____________
Alg2/Trig
Review for Trig Quiz
1. Sketch the given angle in standard position on the axes provided. Then determine the
Measure of the reference angle.
a)
135
b)
c)
ref
= _______
ref
2.
Which of the following is the reference angle for the angle measuring 255 ?
(1) 75
(2) 15
(3) 105
(4) 45
120
= _______
ref
330
= _______
3. Find the smallest positive angle that is coterminal to -413 . __________
4. Which pair of angles is coterminal?
(1)
240 and 210
(2) 225 and  45
(3)
330 and 30
(4)
60 and  60

3 1
, 
5. In the accompanying diagram of a unit circle, the ordered pair  
 2
2 

represents the terminal side of  intersects the unit circle. What is m ?
m = _________________
6. If sin x =
1
3
and cos x = 
, the possible measure of
2
2
x is ______________.
7. If  is an angle in standard position and its terminal side passes through the
 3 1 
point 
on the unit circle, a possible value of  is
 2 , 2 


(1) 30
(2) 60
(3) 300
(4) 330
8. If sin x 
(1) 45
2
and tan x  1 , the measure of angle x is
2
(2) 135
(3) 225
(4) 315
9. On the unit circle shown in the diagram below, sketch an angle, in standard position,
whose degree measure is 120, and then find the exact value of sin120 .


10. Given f  x   tan x , evaluate f 60 .
11. Give the exact value of 2sin 210  cos300 . Show work.
 is an angle in standard position and its terminal side passes through the point
1 3
( , ) on a unit circle, a possible value of  is
2 2
12. If
(1) 30
(2) 60
(3) 120
(4) 150
13. Name an angle that has an exact sine value of 1.
________
14. Expressed as a function of a positive acute angle, tan150 is equal to
(1) tan30
(2)  tan30
(3) tan60
(4)  tan60
15. Find the exact value of each of the following.
a.
cos150
b.
c.
tan240
d. cos30
e.
sin  135
g.
sec210

f.
cot180
sin240
h. tan330
16. If  is an angle in standard position and its terminal side passes through the point
(0.3, -0.6) on a unit circle, what is the value of sin  ?
(1) 0.3
(2) -0.6
(3) -2
(4) -1/2
17. If  is an angle in standard position and its terminal side passes through the point
(-0.94, 0.34) on a unit circle, what is the value of cos ?
0.34
0.94
(1) -0.94
(2) 0.34
(3)
(4)
0.34
0.94
18. Point P is located at the intersection of the unit circle and the terminal side of
 = 123º. Find the coordinates of P to the nearest thousandth.
19. Point P is located at the intersection of a circle with a radius of 5 and
the terminal side of  = 225º. Find the exact coordinates of P.
20. If sec  is negative and tan  is negative, the terminal side of
quadrant__________.
21.
 lie in
If sin  is negative and cos  is positive, in which quadrant does the terminal side
of  lie?
22. The terminal side of  in standard position contains the point (4, -2). Find the
exact value of sin  in simplest form. Show work.
1
23. The terminal side of  lies in quadrant III and sin    . Find the exact value of
3
cos  in simplest form. Show work.
1.
2.
3.
4.
5.
6.
7.
8.
a. 45
(1)
307
(3)
210
150
(4)
(2)
9.
3
2
10.
11.
12.
13.
14.
3
3
2
(2)
90
(2)
b. 60
c. 30
15. a.
c.
 3
2
b. undefined
3
d.
3
2
 3
f.
2
 3
h.
3
 2
2
2 3
g.
3
16. (2)
17. (1)
18. (-0.545, 0.839)
 5 2 5 2 
19. 
,

 2

2


20. II
21. IV
e.
 5
5
2 2
23.
3
22.