Chapter 4 Trigonometric Functions

Trigonometric Functions
98. The average rate of change is the slope of the line
through the points ( x1, g( x
1)
) and ( x2, g( x
2)
)
gx (
2) − gx (
1)
m =
x2 − x1
⎛3π
⎞
cos ( π ) − cos ⎜
4
⎟
=
⎝ ⎠
3π
π −
4
⎛ 2 ⎞
−1− ⎜
−
2 ⎟
=
⎝ ⎠
π
4
⎛ 2 ⎞
4 − 1+
⎜
2 ⎟
=
⎝ ⎠
⎛π
⎞
4⎜
4
⎟
⎝ ⎠
2 2 − 4
=
π
99.
2
π
sinθ = when the reference angle is and θ is
2
4
in quadrants I or II.
QI
QII
π
π
θ = θ = π −
4 4
3π
=
4
π 3π
θ = ,
4 4
1
π
100. cosθ = when the reference angle is and θ is in
2
3
quadrants I or IV.
QI
QIV
π
π
θ = θ = 2π
−
3 3
5π
=
3
π 5π
θ = ,
3 3
2
π
101. sinθ =− when the reference angle is and
2
4
θ is in quadrants III or IV.
QIII
QIV
π
π
θ = π + θ = 2π
−
4 4
5π
7π
= =
4 4
5π
7π
θ = ,
4 4
1
π
102. cosθ =− when the reference angle is and θ is
2
3
in quadrants II or III.
QII
QIII
π
π
θ = π − θ = π +
3 3
2π
4π
= =
3 3
2π
4π
θ = ,
3 3
π
103. tanθ =− 3 when the reference angle is and θ is 3
in quadrants II or IV.
QII
QIV
π
π
θ = π − θ = 2π
−
3 3
2π
5π
= =
3 3
2π
5π
θ = ,
3 3
3
π
104. tanθ =− when the reference angle is and
3
6
θ is in quadrants II or IV.
QII
QIV
π
π
θ = π − θ = 2π
−
6 6
5π
11π
= =
6 6
5π
11π
θ = ,
6 6
105. – 109. Answers may vary.
110. does not make sense; Explanations will vary.
Sample explanation: Sine is defined for all values of
the angle.
530
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