Slope of polar curve

Apr 2009
83
0
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?
 

Prove It

MHF Helper
Aug 2008
12,883
4,999
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 \(\displaystyle \theta = \frac{\pi}{4}\)

\(\displaystyle \frac{dr}{d\theta} = -8\sin{\frac{\pi}{4}}\)

\(\displaystyle = -8\left(\frac{\sqrt{2}}{2}\right)\)

\(\displaystyle = -4\sqrt{2}\).
 
Apr 2009
83
0
yes that is what i got but the answer is 1-radical 2
 
Apr 2009
83
0
weird. i didn't copy the problem wrong. it must be a coincidence because it seems the problem after that is wrong too