Find the slope of the cardioid r=2+2cos(theta) at the point corresponding to (theta)=pi/4

Question

irishboy123 · Answer

$r=2+2cos(\theta)$

the slope takes you back into cartesian, ok?

so you want $\frac{dy}{dx}$

yep?

anonymous · Answer

This one specifically is nothing like the ones I've done in my previous assignment. So I'm confused as to how to even begin to tackle it.

anonymous · Answer

wouldn't the tangent of pi/4 in this case be the slope?

irishboy123 · Answer

totally

irishboy123 · Answer

do you know how to do that?

irishboy123 · Answer

this is it https://www.desmos.com/calculator/qysgdfnvnr

anonymous · Answer

totally makes sense now that I have the graph! thanks!

irishboy123 · Answer

cool!

anonymous · Answer

I have one more question. Maybe you can help with this one too, because MacLaurin Series are my weakest topic in this course so far.

irishboy123 · Answer

just to complete this thread, the formula to get the slope in cartesian is 

$\large \frac{dy}{dx} = \frac{\frac {d r}{d \theta} \ sin \theta + r \ cos \theta}{\frac {d r}{d \theta} \ cos \theta - r sin \theta}$

very deriveable....from the basic premises that $x = r cos \theta $ etc

irishboy123 · Answer

maclaurin

no worries

stick it in a new thread first, though