MATHEMATICS · Single correct · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions
Problem
For a differentiable polar curve described by r=f(θ), which of the following expressions is equal to dxdy in terms of derivatives with respect to θ?
(a) \displaystyle \frac{dr}{d\theta}\sin\theta + r\cos\theta
(b) \displaystyle \frac{\dfrac{dx}{d\theta}}{\dfrac{dy}{d\theta}}
(c) \displaystyle \frac{\dfrac{dy}{d\theta}}{\dfrac{dx}{d\theta}}
(d) \displaystyle \frac{\dfrac{dr}{d\theta}\sin\theta}{\dfrac{dr}{d\theta}\cos\theta}