For a polar curve given by with

MATHEMATICS · Single correct · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions

Problem

For a polar curve given by

r = f(\theta)

with

r\ne 0

, which of the following sets of conditions guarantees that the tangent line to the curve at angle

\theta

is vertical? (a)

\dfrac{dy}{d\theta}=0 \text{ and } \dfrac{dx}{d\theta}\ne 0

(b)

\dfrac{dx}{d\theta}=0 \text{ and } \dfrac{dy}{d\theta}\ne 0

(c)

\dfrac{dy}{dx}=0

(d)

\dfrac{dx}{d\theta}=0 \text{ and } \dfrac{dy}{d\theta}=0