Rectangular to polar equations

• Dec 15th 2008, 08:11 PM
Xenomorph
Rectangular to polar equations
8x+7y=5

How do I change this rectangular equation to polar form!

• Dec 15th 2008, 08:50 PM
Soroban
Hello, Xenomorph!

Quote:

Write in polar form: . $8x+7y\:=\:5$
You're expect to know these conversions: . $\begin{Bmatrix}x &=& r\cos\theta \\ y &=& r\sin\theta \end{Bmatrix}$

Then . $8x + 7y \:=\:5$ becomes: . $8r\cos\theta + 7r\sin\theta \:=\:5$

. . Factor: . $r(8\cos\theta + 7\sin\theta) \:=\:5$

Therefore: . $\boxed{r \;=\;\frac{5}{8\cos\theta + 7\sin\theta}}$