# Thread: 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 $\displaystyle r=cos^3(\theta)$ at the point corresponding to $\displaystyle \theta=\frac{\pi}{4}$

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

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

I will calculate $\displaystyle \frac{dy}{dx}$ at $\displaystyle \theta=\frac{\pi}{4}$ , 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 :
$\displaystyle y-y1=m(x-x1)$

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

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

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

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

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