Chapter 4 Trigonometric Functions

Trigonometric Functions
39.
40.
41.
42.
43.
44.
45.
9π ⎛π ⎞ π 2
cos = cos 2π
cos
4
⎜ +
4
⎟= =
⎝ ⎠ 4 2
9π ⎛π ⎞ π
csc = csc 2π
csc 2
4
⎜ + = =
4
⎟
⎝ ⎠ 4
⎛ 9π ⎞ ⎛ 9π ⎞ 7π
2
sin ⎜− sin 4π
sin
4
⎟= ⎜− + = = −
4
⎟
⎝ ⎠ ⎝ ⎠ 4 2
⎛ 9π ⎞ ⎛ 9π ⎞ 7π
sec⎜− sec 4π
sec 2
4
⎟= ⎜− + = =
4
⎟
⎝ ⎠ ⎝ ⎠ 4
5π ⎛π ⎞ π
tan = tan π tan 1
4
⎜ + = =
4
⎟
⎝ ⎠ 4
5π ⎛π ⎞ π
cot = cot π cot 1
4
⎜ + = =
4
⎟
⎝ ⎠ 4
⎛ 5π ⎞ ⎛3π ⎞ 3π
cot ⎜− cot 2π
cot 1
4
⎟= ⎜ − = = −
4
⎟
⎝ ⎠ ⎝ ⎠ 4
⎛ π ⎞ ⎛ π ⎞
51. cos ⎜− − 1000π
cos 2π
4
⎟ = ⎜− +
4
⎟
⎝ ⎠ ⎝ ⎠
7π
= cos 4
2
=
2
⎛ π ⎞ ⎛ π ⎞
52. cos ⎜− − 2000π
cos 2π
4
⎟ = ⎜− +
4
⎟
⎝ ⎠ ⎝ ⎠
7π
= cos 4
2
=
2
53. a.
b.
3π 2
sin = 4 2
11π ⎛3π ⎞ 3π
2
sin = sin 2π
sin
4
⎜ +
4
⎟ = =
⎝ ⎠ 4 2
46.
⎛ 9π ⎞ ⎛ 9π ⎞ 3π
tan ⎜− tan 3π
tan 1
4
⎟ = ⎜− + = = −
4
⎟
⎝ ⎠ ⎝ ⎠ 4
54. a.
3π 2
cos =− 4 2
⎛π
⎞ π
47. − tan ⎜ + 15π
=− tan = −1
4
⎟
⎝ ⎠ 4
b.
11π ⎛3π ⎞ 3π
2
cos = cos 2π
cos
4
⎜ +
4
⎟= =−
⎝ ⎠ 4 2
⎛π
⎞ π
48. − cot ⎜ + 17π
=− cot = −1
4
⎟
⎝ ⎠ 4
⎛ π ⎞ ⎛ π ⎞
49. sin ⎜− − 1000π
sin 2π
4
⎟= ⎜− +
4
⎟
⎝ ⎠ ⎝ ⎠
7π
= sin 4
2
=−
2
⎛ π ⎞ ⎛ π ⎞
50. sin ⎜− − 2000π
sin 2π
4
⎟= ⎜− +
4
⎟
⎝ ⎠ ⎝ ⎠
7π
= sin 4
2
=−
2
π
55. a. cos = 0
2
b.
π
56. a. sin = 1
2
b.
9π
⎛π
⎞
cos = cos 4
2
⎜ + π
2
⎟
⎝ ⎠
⎡π
⎤
= cos ⎢ + 2(2 π )
2
⎥
⎣ ⎦
π
= cos 2
= 0
9π ⎛π ⎞ π
sin = sin 4π
sin 1
2
⎜ + = =
2
⎟
⎝ ⎠ 2
502
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