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Rates of Change of Trigonometric Functions
Related Topics
Wize High School Grade 12 Pre-Calculus Textbook > Rates of Change
Rates of Change of Trigonometric Functions
5 Activities
Practice: Rates of Change of Trigonometric Functions
A yo-yo oscillates and
d
(
t
)
=
cos
(
11
π
6
t
)
d(t)=\cos\Big(\dfrac{11\pi{}}{6}t\Big)
d
(
t
)
=
cos
(
6
11
π
t
)
represents the displacement of the yo-yo in meters.
a. Determine the average rate of change of the displacement of the yo-yo over the first
5
5
5
minutes. (Do not include units)
b. Determine the instantaneous rate of change when
t
=
5
t=5
t
=
5
minutes. Let
h
=
0.001
h=0.001
h
=
0.001
. Round to the nearest thousandth. (Do not include units)
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More Rates of Change of Trigonometric Functions Questions:
Rates of Change of Trigonometric Functions
Practice: Rates of Change of Trigonometric Functions
Let
y
=
−
cos
θ
y=-\cos{\theta}
y
=
−
cos
θ
.
Rates of Change of Trigonometric Functions
Practice: Rates of Change of Trigonometric Functions
Let
y
=
sin
2
θ
y=\sin{2\theta}
y
=
sin
2
θ
.
Rates of Change of Trigonometric Functions
Practice: Rates of Change of Trigonometric Functions
Cary set out on his bicycle to begin training for the Gran Fondo. The following represents the displacement of the bicycle from the starting point in km:
d
(
t
)
=
sin
(
7
π
6
t
)
d(t)=\sin\Big(\dfrac{7\pi{}}{6}t\Big)
d
(
t
)
=
sin
(
6
7
π
t
)
Rates of Change of Trigonometric Functions
Practice: Rates of Change of Trigonometric Functions
Determine the average rate of change of the function
f
(
θ
)
=
tan
(
π
−
4
θ
)
f(\theta)=\tan(\pi-4\theta)
f
(
θ
)
=
tan
(
π
−
4
θ
)
on the interval
−
π
4
≤
θ
≤
2
π
3
-\dfrac{\pi}{4}\leq{}\theta\leq{}\dfrac{2\pi}{3}
−
4
π
≤
θ
≤
3
2
π
.
Rates of Change of Trigonometric Functions
Practice: Rates of Change of Trigonometric Functions
Determine the average rate of change of the function
f
(
θ
)
=
sin
(
2
θ
+
3
π
)
+
1
f(\theta)=\sin(2\theta+3\pi)+1
f
(
θ
)
=
sin
(
2
θ
+
3
π
)
+
1
on the interval
π
6
≤
θ
≤
5
π
6
\dfrac{\pi}{6}\leq{}\theta\leq{}\dfrac{5\pi}{6}
6
π
≤
θ
≤
6
5
π
.