Find the equation of the tangent to the curve r = θ when θ = π 2 .

Answer 1

y=r(θ)sin(θ),,,,dy/dθ=r'sinθ+rcosθ,,,,at π/2, y=π/2, dy/dθ=1

x=r(θ)cos(θ),,,,dx/dθ=r'cosθ-rsinθ,,,,at π/2, x=0, dx/dθ=-π/2

see dy/dx=[dy/dθ]/[dx/dθ] at π/2, dy/dx=-2/π

line equation is y=[-2/π]x+π/2

if you ever need d²y/dx², the second derivative, when given r=f(θ)

be careful, it is not simply [d²y/dθ²]/[d²x/dθ²]