College Trigonometry, 2011a

788 Foundations of Trigonometry
25. (a) csc(α − β) =− 5 4
(b) sec(α + β) = 125
117
(c) cot(α + β) = 117
44
39. cos(75 ◦ )=
√
2 −
√
3
2
√
2 −
√
2
40. sin(105 ◦ )=
√
2+
√
3
2
41. cos(67.5 ◦ )=
2
√
43. tan(112.5 ◦ )=−
2+ √ 2
2 − √ 2 = −1 − √ 2 44. cos
42. sin(157.5 ◦ )=
( ) 7π
= −
12
√
2 −
√
2
2
√ √
2 − 3
2
√
( √
π 2 − 3
45. sin =
12)
2
( ) √ √
5π 2+ 2
47. sin =
8 2
√
( π
) √
2+ 2
46. cos =
8 2
( 7π
48. tan
8
)
√
= −
2 − √ 2
2+ √ 2 =1− √ 2
49. ˆ sin(2θ) =− 336
625
ˆ sin ( √
)
θ 2
2 =
10
50. ˆ sin(2θ) = 2520
2809
ˆ sin ( )
θ 5 √ 106
2 =
106
51. ˆ sin(2θ) = 120
169
ˆ sin ( )
θ 3 √ 13
2 =
13
√
15
52. ˆ sin(2θ) =−
8
ˆ sin ( √ √
)
θ 8+2 15
2 =
4
53. ˆ sin(2θ) = 24
25
ˆ sin ( √
)
θ 5
2 =
5
ˆ cos(2θ) = 527
625
ˆ cos ( )
θ 7 √ 2
2 = −
10
ˆ cos(2θ) =− 1241
2809
ˆ cos ( )
θ 9 √ 106
2 =
106
ˆ cos(2θ) =− 119
169
ˆ cos ( )
θ 2 √ 13
2 = −
13
ˆ cos(2θ) = 7 8
ˆ cos ( √ √
)
θ 8 − 2 15
2 =
4
ˆ cos(2θ) =− 7 25
ˆ cos ( )
θ 2 √ 5
2 =
5
ˆ tan(2θ) =− 336
527
ˆ tan ( )
θ 1
2 = −
7
ˆ tan(2θ) =− 2520
1241
ˆ tan ( )
θ 5
2 =
9
ˆ tan(2θ) =− 120
119
ˆ tan ( )
θ 3
2 = −
2
√
15
ˆ tan(2θ) =−
7
ˆ tan ( )
θ
√8+2 √ 15
2 =
8 − 2 √ 15
tan ( √
θ
2)
=4+ 15
ˆ tan(2θ) =− 24 7
ˆ tan ( θ
2
)
=
1
2