Rates of Change in Polar Functions
AP Precalculus · Flashcards · Application
AP PRECALCULUS · FLASHCARDS
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QUESTION
Find
d
y
d
θ
\frac{dy}{d\theta}
d
θ
d
y
for
r
(
θ
)
=
1
+
cos
(
θ
)
r(\theta) = 1 + \cos(\theta)
r
(
θ
)
=
1
+
cos
(
θ
)
.
QUESTION
Find
d
y
d
θ
\frac{dy}{d\theta}
d
θ
d
y
for
r
(
θ
)
=
θ
2
r(\theta) = \theta^2
r
(
θ
)
=
θ
2
.
QUESTION
What is the formula for
d
x
d
θ
\frac{dx}{d\theta}
d
θ
d
x
when
r
=
sin
(
θ
)
r = \sin(\theta)
r
=
sin
(
θ
)
?
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ANSWER
d
x
d
θ
=
cos
(
θ
)
cos
(
θ
)
−
sin
2
(
θ
)
\frac{dx}{d\theta} = \cos(\theta)\cos(\theta) - \sin^2(\theta)
d
θ
d
x
=
cos
(
θ
)
cos
(
θ
)
−
sin
2
(
θ
)
. Substitute
r
=
sin
(
θ
)
r = \sin(\theta)
r
=
sin
(
θ
)
and
d
r
d
θ
=
cos
(
θ
)
\frac{dr}{d\theta} = \cos(\theta)
d
θ
d
r
=
cos
(
θ
)
into formula.
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