Converting a Polar Equation to Rectangular

**Kimberley** · April 5th 2011, 08:29 AM

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.

**FernandoRevilla** · April 5th 2011, 09:04 AM

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.

**Kimberley** · April 5th 2011, 09:11 AM

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.

**FernandoRevilla** · April 5th 2011, 09:33 AM

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 $y=\sqrt{3}x\;(x<0)$

**HallsofIvy** · April 5th 2011, 09:36 AM

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 $y= tan(\theta)x$ .

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