# Converting a Polar Equation to Rectangular

• April 5th 2011, 08:29 AM
Kimberley
Converting a Polar Equation to Rectangular
Hello, I do need help with a particular problem in my homework.

The problem is theta = 4pi/3.

I need to convert this equation to a rectangular equation.

I get so antsy seeing theta = instead of r =. (Worried)

Thanks in advance to anyone who responds. (Happy)
• April 5th 2011, 09:04 AM
FernandoRevilla
Quote:

Originally Posted by Kimberley
The problem is theta = 4pi/3. I need to convert this equation to a rectangular equation.

Hint : Corresponds to a half line. Find the equation.
• April 5th 2011, 09:11 AM
Kimberley
Quote:

Originally Posted by FernandoRevilla
Hint : Corresponds to a half line. Find the equation.

Yes, I know what the equation is but I do not know how to convert the original equation algebraically. And that is what I need to do.
• April 5th 2011, 09:33 AM
FernandoRevilla
Quote:

Originally Posted by Kimberley
Yes, I know what the equation is but I do not know how to convert the original equation algebraically. And that is what I need to do.

$y=\tan (4\pi/3)x\;(x<0)$ or $y=\sqrt{3}x\;(x<0)$
• April 5th 2011, 09:36 AM
HallsofIvy
Hopefully, you know that $x= r cos(\theta)$ and $y= r sin(\theta)$. From those, $\frac{sin(\theta)}{cos(\theta)}= tan(\theta)= \frac{y}{x}$ and so $y= tan(\theta)x$.