Find the slope of the tangent line to polar curve

Question

Find the slope of the tangent line to polar curve r=6sin(theta) at the point (6/2 , pi/6)

Answer 1

The Cartesian equation of the function is x² +(y-3)² = 9

x= 6 sin θ cos θ and y = 6 sin²θ

At the given point x=1.5√3 and y =1.5

dy/dx=-x/(y-3) and at the given point dy/dx=√3

The equation of the tangent line is y=1.5+(x-1.5√3)√3