For a polar curve

MATHEMATICS · Subjective · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

For a polar curve

r=f(\theta)

, explain why a value of

\theta

at which

\dfrac{dy}{d\theta}=0

while

\dfrac{dx}{d\theta}\neq 0

corresponds to a horizontal tangent line to the curve in rectangular coordinates.