Question

how to find the highest point on the cardioid r = 1 + cos θ.

Answer 1

when you say the highest point, you mean, maximum "y" value?

Answer 2

yeah i thnk soo

Answer 3

or the maximum "r" = distance of outermost point from the center?

Answer 4

not sure bt da answer shud cme to (3/2, π/3)...dnt knw how??

Answer 5

ok
\[r(\theta)=1+\cos\theta\\y(\theta)=r(\theta)\cdot\sin\theta\\\implies y(\theta)=\sin\theta+\cos\theta\sin\theta\]
we are maximizing "y" with theta.
os, its first derivative is "0"

Answer 6

\[y'=\cos\theta+\cos^2\theta-\sin^2\theta=0\\\cos\theta+\cos^2\theta-(1-\cos^2\theta)=0\]
solve for theta

Answer 7

ohhhk.. thanks alot...

Answer 8

yw