math question please help

Question

Find the slope of the tangent line to the given polar curve at the point specified by the value of 𝜃, 𝑟 = 1 + cos 𝜃 , 𝜃 = 𝜋/ 6.

Answer 1

r = 1 + cosθ = f(θ)

f'(θ) = -sinθ

At θ = π/6, f(θ) = 1 + √3/2 and f'(θ) = -1/2

dy/dx = [f'(θ)sinθ + f(θ)cosθ] / [f'(θ)cosθ - f(θ)sinθ]

= [(-1/2)(1/2) + (1+√3/2)(√3/2)] / [(-1/2)(√3/2) - (1+√3/2)(1/2)]

= [(1+√3)/2] / [(-1-√3)/2] = (1+√3)/(-1-√3) = -1