Find the slope of the curve r=cos(2theta) at theta=pi/6.. must this be solved parametrically? if so, why?

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 .

45

step-by-step explanation:

to find a percentage, add a decimal in front and multiply it by the other number.

.25 times 180= 45