Find the slope of the polar curve at the indicated point.
-$$r = \csc \theta , \theta = \frac { \pi } { 6 }$$
A) 0
B) -1
C) 1
D) Undefined

Question

Quizplus · Accepted Answer

The slope of a polar curve $ r = f(\theta) $ at a point is given by $\frac{dy}{dx} = \frac{r' \sin \theta + r \cos \theta}{r' \cos \theta - r \sin \theta}$. For $ r = \csc \theta $, $ r' = -\csc \theta \cot \theta $. At $\theta = \frac{\pi}{6}$, $ r = 2 $, $ r' = -2\sqrt{3} $, and substituting these into the slope formula gives 0.

Find the Slope of the Polar Curve at the Indicated r=csc⁡θ,θ=π6r = \csc \theta , \theta = \frac { \pi } { 6 }r=cscθ,θ=6π​

Find the Slope of the Polar Curve at the Indicated $r = \csc \theta , \theta = \frac { \pi } { 6 }$