# Math Help - Equation of tangent line (rec. form) to a polar curve!!

1. ## Equation of tangent line (rec. form) to a polar curve!!

Hello
Quesiton:
Find the rectangular form of the equation of the tangent line to the polar curve $r=cos^3(\theta)$ at the point corresponding to $\theta=\frac{\pi}{4}$

How to do that?
I mean finding it in RECTANGULAR FORM !

i know that $\frac{dy}{dx}=\frac{\frac{dr}{d\theta} sin(\theta)+rcos(\theta)}{\frac{dr}{d\theta} cos(\theta) - r sin(\theta)}$

I will calculate $\frac{dy}{dx}$ at $\theta=\frac{\pi}{4}$ , and this is easy ..
The problem here is that, how can I find the equation of the tangent line in RECATNGULAR FORM ??

The equation of the tangent line is :
$y-y1=m(x-x1)$

m = the slope , and this one will be calculated by using the formula ..
but what about x1 and y1?

2. $r =\cos^3{\theta}$

$x = r\cos{\theta} = \cos^4{\theta}$

$y = r\sin{\theta} = \cos^3{\theta} \sin{\theta}
$

sub in $\frac{\pi}{4}$ for $\theta$ to determine x and y