NAME_________________________________________DATE___________________
ALGEBRA2
MRS. BINASO
CHAPTER 15: TRIGONOMETRIC IDENTITIES AND EQUATIONS
Show all work on loose leaf.
4
1. If sin θ =
and θ is located in quadrant I, find cos θ.
5
2. If cos θ =
1
and θ is located in quadrant IV, find sin θ.
4
3. If sin θ =
5
and tan θ < 0, find cos θ.
13
4. If cos θ =
5
and θ is located in quadrant III, find sin θ and tan θ.
13
Express each of the following as a single term containing one function or constant.
5. sin x cot x
6. sin θ csc θ cot θ
7. cos x tan x csc x
8. 2 – 2cos2θ
9. cos x (1 + tan2x)
10. cos θ sec θ – cos2θ
11.
cos
sec 
12.
csc 
cot 
13.
cos tan 
sin  sec 
14.
sin 2   1
cos
15.
csc   sin 
cot 
16.
tan 2 x  sin 2 x
sin 2 x
19.
sin 2 x  cos2 x
 sec x
cos x
Prove that each of the following equations is an identity.
17. tan x cos x = sin x
20. cot  
18. tan x csc x = sec x
csc 
sec 
21. sin θ + cot θ cos θ = csc θ
22. 1 – cos2x = sin x cos x tan x
23. (sin x – cos x)2 = 1 – 2 sin x cos x
24. cos2x = sec2x – tan2x – sin2x
25.
sec  sin 

 cos csc 
sin  cos
26. sin 2x = 2 cot x sin2x
27.
1  cos 2
 cos
2 cos
sin 2 x
28. tan x 
1  cos 2 x
2 sin 2 A
 cot A  sec A csc A
29.
sin 2 A
Solve each equation for all values of the variable in the interval between 0˚ and 360˚.
30. 3 cos θ = cos θ – 1
31. -2 sin θ – 2 = 0
32. 3 cos θ + 5 = 0
33. 3(sin θ – 1) = 0
34. cot θ + 2 = 2 cot θ + 3
35. cos2θ – cos θ = 0
36. sin2θ + 3 sin θ + 2 = 0
37. cos2θ – 2 cos θ = 3
38. sec2θ = sec θ + 2
39. 3 sin θ +
1
=4
sin 
40. cos2θ – cos θ + 3 = 0
41. sin2θ + 5 sin θ – 1 = 0
42. cos2θ = 3 cos θ – 1
43. sin2θ + 4 cos θ = 3
44. 2 cos2θ + 3 sin θ = 0
45. cos θ – sin2θ = 1
46. cos 2θ + cos θ = 0
47. 2 sin θ = 2 + cos 2θ
48. cos 2θ = cos θ + 2
Express each of the following in terms of sin θ or cos θ.
3

49. sin (θ – π)
50. cos
2
4
5
If sin x = , sin y =
, and x and y are each in quadrant I, find the value of each of
5
13
the following.
F
IJ
G
H K
51. sin (x + y)
52. cos (x – y)
53. tan (x + y)
Given the following values, find cos 2θ.
3
1
54. sin θ =
55. cos θ =
5
3
Find each value.
2
1
1
56. arcsin
57. Arc sin
58. arc cos
2
2
2
59. Arc cos
1
2
62. sin (Arc tan 1)
F 3 I
G
H2 JK
LArc cosF3 IO
63. sin M
H2 J
KP
M
P
N G
Q
60. Arc sin
61. arc tan
F 3 I
G
H3 JK
F
G
H
64. sin Arc cos
15
17
IJ
K