Question

Find dy/dx if x=cos theta and y= sin theta at theta=pi/4

Answer 1

Given that

x = cosθ, y = sinθ

Differentiate x and y with respect to  θ, we get

dx/dθ = -sinθ       and dy/dθ = cosθ       ...(1)

Now evaluate dy/dx

dy/dx = [(dy/dθ)/(dx/dθ)]                   { using chain rule ]

⇒ dy/dx = (cosθ)/(-sinθ)

⇒ dy/dx = -cotθ

At θ = π/4,

⇒ dy/dx = -cot(π/4)

⇒ dy/dx = -1