Find the slope of the polar curve at the indicated point.
-$$\mathrm { r } = 9 + 3 \sin \theta , \theta = 0$$
A) $- \frac { 1 } { 3 }$
B) $- 3$
C) 3
D) $\frac { 1 } { 3 }$

Question

Quizplus · Accepted Answer

To find the slope of the polar curve, we need to differentiate the polar equation with respect to $	heta$.

\begin{align*}
\frac{d}{d	heta}\left(right)&=\frac{d}{d	heta}\left(9+3\sin	hetaight)\
\frac{dr}{d	heta}&=3\cos	heta
\end{align*}

At $	heta=0$, we have $\frac{dr}{d	heta}=3\cos(0)=3$. This is the slope of the tangent line at that point. Therefore, the answer is C.

Find the Slope of the Polar Curve at the Indicated r=9+3sin⁡θ,θ=0\mathrm { r } = 9 + 3 \sin \theta , \theta = 0r=9+3sinθ,θ=0

Find the Slope of the Polar Curve at the Indicated $\mathrm { r } = 9 + 3 \sin \theta , \theta = 0$