Question

If y =1 − cos θ, x = 1 − sin θ, then `dy/dx  "at"  θ =pi/4` is ______

Answer 1

If y =1 − cos θ, x = 1 − sin θ, then `dy/dx  "at"  θ =pi/4` is −1

Explanation:

Given:

y = 1 − cosθ, x = 1 − sinθ

Differentiate w.r.t. θ

`dy/(d theta) = sin theta`

`dx/(d theta) = -cos theta`

`dy/dx = (dy/(d theta))/(dx/(d theta)) = sin theta/-cos theta = - tan theta`

`dy/dx = -tan (pi/4) =-1`

`dy/dx` at θ = π/4 = −1