Find the slope of the tangent line at theta=pi/2?

Question

Find the slope of the tangent line at theta=pi/2 for the curve in the xy plane with the polar equation r=theta.

Answer 1

y = r sinθ = θ sinθ

y(pi/2) = pi/2

y'(pi/2) = sinθ + θcosθ at θ=pi/2 = 1

x = r cosθ = θ cosθ

x(pi/2) = 0

x'(pi/2) = cosθ - θsinθ at θ=pi/2 = -pi/2

slope = dy/dx = y'(pi/2)/x'(pi/2) = -2/pi

Answer in point-slope form: y - pi/2 = (-2/pi)(x - 0)