Find the slope of the polar curve at the indicated point.
r=8(1+cos theta) theta=pi/4
I must be doing it wrong because I took the derivative of r and got:
dr/dtheta = -8sin theta= -4 radical 2.
The answer is 1-radical 2
Whats my error?
Find the slope of the polar curve at the indicated point.
r=8(1+cos theta) theta=pi/4
I must be doing it wrong because I took the derivative of r and got:
dr/dtheta = -8sin theta= -4 radical 2.
The answer is 1-radical 2
Whats my error?
$\displaystyle r = 8(1 + \cos{\theta})$
$\displaystyle \frac{dr}{d\theta} = -8\sin{\theta}$.
So when $\displaystyle \theta = \frac{\pi}{4}$
$\displaystyle \frac{dr}{d\theta} = -8\sin{\frac{\pi}{4}}$
$\displaystyle = -8\left(\frac{\sqrt{2}}{2}\right)$
$\displaystyle = -4\sqrt{2}$.