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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
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
.
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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
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.
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
.