ALGEBRA III/TRIG CP - FINAL REVIEW
NAME __________________________
CHAPTER 4
Evaluate each. Round to 3 decimal places when necessary.
11
__________ b) 6 _________
9
2) Change to radian measure: a) 28.45 _________ b) 248.26 _________
1) Change to degrees: a)
3) Change to radians as a multiple of  : a) 210 ________ b) 315 ________
4) Find the quadrant that the terminal side of  would be in when drawn in standard
position.
5
14
a)   130 ________
b)  
________
c)   
________
7
9
5) Find a positive angle < 360 that is coterminal with: a) 740 ______ b) 910 ______
6) Find a cofunction with the same value as
a) cos10 _________ b) csc82 _________
7) Find the length of an arc of a circle with a) radius 8.3 cm. and central angle
5
_______
7
b) radius 2.6 m. and central angle 38.9 _______
 3 
8) Find: a) cos  
 _________
 8 
b) csc
9
3
_________ c) sin   _________
5
4
9) Find: a) sin148.491 ________ b) cot  265.44 _______ c) csc(122.8) ________
10) Find   0    90 given that:
a) tan   3.48 ________ b) sin  .9435 _________
c) sec x  2.819 ________


11) Find the angle, x, with  0  x   given that:
2

a) cos  .4551 ________ b) cot x  .9435 ________ c) csc x  2.1973 _________
Given right triangle ABC,
A
c
b
C
a
B
12) A  42, a  5
solve for b.
__________________
13) a  21.3, c  34.8
solve for B.
__________________
Page 1 of 8
Draw a diagram for each and solve. Continue to round to 3 decimal places when necessary.
14) A 10 foot ladder leaning against the side of a house makes a 65
angle with the ground. Show all work and explain.
a) How far is the base of the ladder from the house?
b) If the ladder slides down the side of the house, how will
this affect the angle with the ground?
15) The length of the shadow of a tree is 100 feet. When the angle of
elevation of the sun is 28 find the height of the tree.
Show all work and explain.
Find the exact value for each in #16-28. (NO decimals!)
3
4
11
18) cot
6
20) cos300
16) sin
22) csc240
_________
17) sec
_________
19) tan
10
3
___________

___________
2
21) cot  270 ___________
_________
 5 
23) cot    ___________
 4 
_________
24) Find tan  given that sin   
2
and 180    270
3
25) Find csc given that sec  
4
and 90    180 _______________
3
26) Find cos  tan 1 3
________________
_______________
27) Find the tan x when csc x 
17
and cos x  0 .
8
28) Find the 2 values of  , 0    2 , that satisfy sin   
Page 2 of 8
___________
1
__________
2
Find the reference angle for each.
29) 235 __________
30)
19
_________
12
31) 124 ________
32) Name the trig functions that are even. _____________________ What does this mean?
33) Name the trig functions that are odd. ______________________ What does this mean?
Find the amplitude, period, and phase shift (horizontal shift) for each:
34) y  2 cos(3x   ) __________________ 35) y  0.5sin( 12 x  2 ) ________________
State the Period for each and graph each of the following in #36-41 for one period! Label
“key” values along the x- and y- axes. Write the domain and range for #38-41.
36) y  3sin
x
2
Period______
Amplitude _______


37) y  2 cos  x  
4

Period______
Amplitude _______
38) y  tan x
Period______
39) y  cot x
Period______
Domain ____________________
Domain ____________________
Range _______________
Range ________________
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41) y  csc  x 
Period______
40) y  sec x
Period______
Domain ____________________
Domain ____________________
Range ________________
Range ________________
Name the domain and range for
42) y  sin 1 x
Domain: ___________
Range: ____________
43) y  cos1 x
Domain: ___________
Range: ____________
44) y  tan 1 x
Domain: ___________
Range: ____________
45) Graph y  sin 1 x
46) Graph y  cos1 x
Evaluate each in terms of  .
47) cos 1
3
2
__________

2
49) sin 1  

 2 
51) cos 1 0
__________
__________
48) tan 1  1
____________
 1
50) cos 1   
 2
____________
52) tan 1 3
___________
Page 4 of 8
CHAPTER 5
Use identities to simplify the given expressions
53) 1  sin 2 x
54) 1  tan 2 x
55) cos(  x)
56) cos(90  x)
Verify each identity.


57) sin  x     cos x
2

 3

 x   2 cos x
58) cos   x   sin 
 2

59) csc2 x(1  cos2 x)  1
60) sin 2 x 
61) cos x  sin x tan x  sec x
62)
csc   x 
sec   x 
2 tan x
1  tan 2 x
  cot x
Page 5 of 8
63) Use a sum and difference formula to simplify:
a. sin110 cos 40  cos110 sin 40
b.
tan140  tan 55
1  tan140 tan 55
64) Use a double angle formula to simplify:
a) cos 2 25  sin 2 25
b) 2sin

7
cos

7
c) 1  2sin 2 70
65) Find the exact value of cos  A  B  given cos A 
4
12
in Q4 and sin B 
in Q2.
5
13
66) Find the exact value of sin 2x if cos x 
24
 3 
and x is in the interval  ,
.
25
2 

67) Find the exact value of cos 2x if sin x 
2
 
and x is in the interval  0,  .
3
 2
Find all solutions in the interval 0, 2  for #68-73. When possible, write answers in terms
of  ; otherwise, round to hundredths.
68) 2sin x 1  0
69) 2sin 2 x  1  0
Page 6 of 8
70) 2sin 2 x  3cos x  3  0
71) cos 2 x  cos x  0
72) 3 tan 2 x  tan x  2  0
73) cos 2x  sin x  0
CHAPTER 6
Find the number of triangles that can be formed given the following information:
74) a. A  33, a  9.4, b  7.5
b. A  25, a  6.1, b  14
c. A  85, a  10, b  25
For #75-77 solve each triangle for the missing sides and angles. Round to tenths.
75) A  56, B  96, b  14
76) a  5, b  11, c  13
Page 7 of 8
77) A  47, b  6.5, c  9
78) Find the area of the triangle from #77 above. Round to tenths.
79) Find the length of the brace (d) required to support the street light shown in the figure. Show
all work and explain. Round to hundredths.
3.5 ft
D
4.5 ft
d
34
ALGEBRA III - TRIGONOMETRY CP FINAL EXAM FORMULA SHEET
The following formulas may be useful:
sin  u  v   sin u cos v  cos u sin v
a
b
c


sin A sin B sin C
cos  u  v   cos u cos v sin u sin v
a 2  b 2  c 2  2bc cos A
tan  u  v  
tan u  tan v
1 tan u tan v
Area  12 ac sin B
sin 2 x  cos 2 x  1
sin 2u  2sin u cos u
1  cot 2 x  csc 2 x
tan 2 x  1  sec 2 x
cos 2u  cos 2 u  sin 2 u
 2 cos 2 u  1
 1  2sin 2 u
tan 2u 
2 tan u
1  tan 2 u
Page 8 of 8
or
cos A 
b2  c 2  a 2
2bc