# Thread: Converting a Polar Equation to Rectangular

1. ## 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 =.

Thanks in advance to anyone who responds.

2. 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.

3. 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.

4. 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.

$\displaystyle y=\tan (4\pi/3)x\;(x<0)$ or $\displaystyle y=\sqrt{3}x\;(x<0)$

5. Hopefully, you know that $\displaystyle x= r cos(\theta)$ and $\displaystyle y= r sin(\theta)$. From those, $\displaystyle \frac{sin(\theta)}{cos(\theta)}= tan(\theta)= \frac{y}{x}$ and so $\displaystyle y= tan(\theta)x$.