Quarter Test Review Seniors
Name_________
1.
Find the values of each of the six trigonometric functions for the angle whose terminal side
passes through the point
10,  7  .
sin   __________
csc  __________
cos  __________
sec  __________
tan   __________
cot   __________
sec315
2.
Find the EXACT value of
3.
Suppose csc    2 and the terminal side of the angle lies in Quadrant III, find sin  .
4.
Suppose csc    2 and the terminal side of the angle lies in Quadrant IV, find cos  .
5.
Suppose
cos 
7
25
without using a calculator. Show your angle and coordinates.
and    
3
, find tan  .
2
6. Let  be an acute angle of a right triangle for which tan  
7.
Find the reference angle for an angle measuring 145  .
8.
Find the EXACT (no decimals) value of
9.
Find the EXACT value of sin
24
. Find the EXACT value of sin  .
7
sin 60  cos45 .
11
7
 tan
.
6
4
10. Find the value of csc t for the angle whose terminal side passes through the point 4,  3 .
11.
Use right triangle ABC to find measure of angle B, and sides a and c.
Round to the nearest tenth and remember to label the diagram.
mB  = ____________
A
a = ____________
c
14
c = _____________
C
a
B
12. From a point 35 feet from the bottom of a oak tree, the angle of elevation to the top of the tree
is
63.7 .
Find the height of the tree to the nearest foot.
13. A 35-foot-long, upward moving escalator has an angle of elevation of 34 . What is the vertical
distance between the floors? Round the answer to the nearest tenth of a foot.
14.
Let  be an angle in standard position. State the quadrant in which the terminal side of  lies.
y
cos  0 , tan   0
x
15. Given the information below, in which quadrant does  lie?
a) sin   0, tan   0
c)   
4
5
a)________
c)________
b) tan   0,     2
b)________
d)   417
d)________
16. Find the two values of  , 0    2 , that satisfy the given trigonometric equation.
a)
2
cos   
2
  ______ , _______
b)
3
3
  ______ , _______
tan   
c)
2 3
3
  ______ , _______
csc   
Verify each identity one step at a time:
17. tanx = sinx secx
18 . csc =
cot 
cos()
Verify each identity one step at a time:
sin 2 x  cos 2 x
19.
= sec2x
cos 2 x
21. cot(90 – x) +
cos x
= secx
1  sin x
23. csc2x tan2x – 1 = tan2x
20.
1
1
–
= -2sec2y
sin y  1 sin y  1
22. (sinu + cosu)2 + (sinu – cosu)2 = 2
24. sin x (csc x – sin x) = cos2 x
Solve the Trig Equations for all possible values of x on the interval 0  x  2
25. cos (x) = ½
26. 4 sin2 x = 3
27. cos (x) = 0
28. 2 cos2x + cos x – 1 = 0
29. sin (x) = 
2
2
30. 3 tan2 x – 1 = 0