Question

Find the slope of the tangent line to the given polar curve at the point specified by the value of θ.

r=6/θ, θ=π

Answer 1

y = r sinθ
x = r cosθ

dy = sinθ dr + r cosθ dθ
dx = cosθ dr - r sinθ dθ

so, the slope of the tangent line is

dy/dx = (sinθ dr + r cosθ dθ)/(cosθ dr - r sinθ dθ)

at θ=π, dy/dx = r dθ/dr = r(-6/r^2) = -π^2/6

so, now we have a point and a slope, so the tangent line is

y = -π^2/6 (x + 6/π)