By converting into parametric equations,
x(θ)=r(θ)cosθ=cos2θcosθ
y(θ)=r(θ)sinθ=cos2θsinθ
By Product Rule,
x'(θ)=−sin2θcosθ−cos2θsinθ
x'(π/2)=−sin(π)cos(π/2)−cos(π)sin(π/2)=1
y'(θ)=−sin2θsinθ+cos2θcosθ
y'(π/2)=−sin(π)sin(π/2)+cos(π)cos(π/2)=0
So, the slope m of the curve can be found by
m=dy/dx∣θ=π2
= y'(π/2)/x'(π/2)
=0/1
=0
I hope my answer has come to your help. Thank you for posting your question here in Brainly.
