Chapter 4 Trigonometric Functions

Trigonometric Functions
75.
76.
π
− lies in quadrant IV. The reference angle is
4
π
θ ′ = .
4
π
tan = 1
4
Because the tangent is negative in quadrant IV,
⎛ π ⎞ π
tan ⎜− ⎟= − tan =−1
⎝ 4 ⎠ 4
π
− lies in quadrant IV. The reference angle is
6
π π 3
θ = . tan =
6 6 3
Because the tangent is negative in quadrant IV,
⎛ π ⎞ 3
tan ⎜− ⎟ =− .
⎝ 6 ⎠ 3
77. sec 495°= sec135°=−
2
78.
79.
80.
2 3
sec510°= sec150°=−
3
19π
7π
cot = cot = 3
6 6
13π
π 3
cot = cot =
3 3 3
87.
π π 3π
sin cosπ − cos sin
3 3 2
⎛ 3 ⎞ ⎛1⎞
= ( −1) − ( −1
⎜
)
2 ⎟ ⎜
2
⎟
⎝ ⎠ ⎝ ⎠
3 1
=− +
2 2
1−
3
=
2
π π
88. sin cos 0 − sin cosπ
4 6
⎛ 2 ⎞ ⎛1⎞
= () 1 − ( −1
⎜
)
2 ⎟ ⎜
2
⎟
⎝ ⎠ ⎝ ⎠
2 1
= +
2 2
2 + 1
=
2
89.
11π 5π 11π 5π
sin cos + cos sin
4 6 4 6
⎛ 2 ⎞⎛ 3 ⎞ ⎛ 2 ⎞⎛1⎞
= − + −
⎜ 2 ⎟⎜ 2 ⎟ ⎜ 2
⎟⎜⎟ 2
⎟
⎝ ⎠⎝ ⎠ ⎝ ⎠ ⎝ ⎠
6 2
=− −
4 4
6 + 2
=−
4
81.
82.
83.
84.
23π
7π
2
cos = cos =
4 4 2
35π
11π
3
cos = cos =
6 6 2
⎛ 17π
⎞ 7π
3
tan ⎜− tan
6
⎟= =
⎝ ⎠ 6 3
⎛ 11π
⎞ π
tan ⎜− = tan = 1
4
⎟
⎝ ⎠ 4
90.
17π 5π 17π 5π
sin cos + cos sin
3 4 3 4
⎛ 3 ⎞⎛ 2 ⎞ ⎛1⎞⎛ 2 ⎞
= − − + −
⎜ 2 ⎟⎜ 2 ⎟ ⎜
2
⎟
⎜ 2 ⎟
⎝ ⎠⎝ ⎠ ⎝ ⎠⎝ ⎠
6 2
= −
4 4
6 − 2
=
4
85.
⎛ 17π
⎞ π 3
sin ⎜− sin
3
⎟ = =
⎝ ⎠ 3 2
86.
⎛ 35π
⎞ π 1
sin ⎜− sin
6
⎟ = =
⎝ ⎠ 6 2
528
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