Question

If x = p sin θ, y = q cos θ, then `dy/dx` = ______ 

Options

• `(-q/p)tan theta`

• `(-p/q)tan theta`

• tan θ

• `(q/p)tan theta`

Answer 1

If x = p sin θ, y = q cos θ, then `dy/dx` = `underline((-q/p)tan theta)`

Explanation:

x = p sin θ, y = q cos θ

∴ `dx/(d theta) = p costheta` and `dy/(d theta) = -q sin theta`

∴ `dy/dx = (dy/(d theta))/(dx/(d theta)) = (-q sintheta)/(p costheta) = (-q/p)tan theta`