Find the slope of the tangent line to the graph of r = 1 + cos θ, at theta equals pi over 6

Question

Find the slope of the tangent line to the graph of r = 1 + cos θ, at  

A	-1
B	0
C	1
D	Undefined

Answer 1

Slope m of tangent line m = dy/dx at θ = π/6.

x = rcosθ = (1 + cosθ)cosθ = cosθ + cos²θ;

y = rsinθ = (1 + cosθ)sinθ = sinθ + 0.5sin2θ.

dy/dx = (dy/dθ)/dx/dθ) = (cosθ + cos2θ)/(- sinθ - sin2θ);

Slope m = (cosπ/6 + cosπ/3)/(- sinπ/6 - sinπ/3) = (√3/2 + 1/2)/(- 1/2 - √3/2) = - 1.

Answer is A