Hi, I need help with math

Question

What is the slope of the line tangent to the polar curve r=4θ^2 at the point where θ=pi/4

a) pi/2

b) pi^2/4

c) 8+pi/8-pi

d) something else?

Answer 1

Θ = t , r = 4t²

x = 4t²cost. , y = 4t²sint

dx/dt = 8tcost - 4t²sint dy/dt = 8tsint + 4t²cost

dy/dx = (8tsint + 4t²cost) / (8tcost - 4t²sint) = - (tcost + 2sint) / (tsint - 2cost)

dy/dx | _t=π/4 = (8 + π) / (8 - π)