Question

Solve for theta

Answer 1

\[0=\frac{ \cos(2\theta)+\cos(\theta) }{ -(\sin(2\theta)+\sin(\theta)) }\]

Answer 2

I mean... I could easily do this with a calculator but I am not allowed to.

Answer 3

a fraction is only zero if the numerator is

Answer 4

I should mention this is actually the derivative of a polar function.

Answer 5

solve \[\cos(2\theta)+\cos(\theta)=0\]

Answer 6

I just can't find the maximums.

Answer 7

use the double angle formula for cosine

Answer 8

That just complicates things.

Answer 9

\[2\cos^2(\theta)-1+\cos(\theta)=\] and solve the quadratic

Answer 10

Find the maximum height above the x -axis of the cardioid r = 2(1 + cos (θ)). That was the original question.

I found the derivative which was that.

Answer 11

Ohh... Okay...