Mathematics

Problem

For a polar curve given by

r=f(\theta)

, which of the following expressions equals the slope

\dfrac{dy}{dx}

in terms of

\theta

? a)

\dfrac{\dfrac{dr}{d\theta}\cos\theta-r\sin\theta}{\dfrac{dr}{d\theta}\sin\theta+r\cos\theta}

\dfrac{\dfrac{dr}{d\theta}\sin\theta+r\cos\theta}{\dfrac{\,dr}{d\theta}\cos\theta+r\sin\theta}

\dfrac{\dfrac{dr}{d\theta}\sin\theta+r\cos\theta}{\dfrac{dr}{d\theta}\cos\theta-r\sin\theta}

\dfrac{\dfrac{dr}{d\theta}\cos\theta+r\sin\theta}{\dfrac{dr}{d\theta}\sin\theta-r\cos\theta}