First recall that
x = rcosθ and y = rsinθ
Thus
x = (2 - sinθ)(cosθ) and y = (2 - sinθ)(sinθ)
Now
dx/dθ = 2(sinθ)^2 - 2sinθ - 1 and dy/dθ = 2cosθ - 2sinθcosθ
Now evaluating each derivative above @ θ = π/3, we obtain
dx/dθ = (1 - 2√3)/2 and dy/dθ = (2 - √3)/2
Now
dy/dx = (dy/dθ)(dθ/dx)
Thus @ θ = π/3,
dy/dx = [(2 - √3)/2][2/(1 - 2√3)]
dy/dx = (2 - √3)/(1 - 2√3) is the slope of the required tangent
