Can someone walk me through converting polar /rectangular coordinates?

**trishajoable** · May 2nd 2012, 06:22 PM

ok here are my two questions. I need to see step by step what i need to do.

convert the following polar equation to rectangular
2cos theta= sintheta+ r

convert the following rectangular equation to polar
3x=y²

**Prove It** · May 2nd 2012, 07:54 PM

Originally Posted by trishajoable

ok here are my two questions. I need to see step by step what i need to do.

convert the following polar equation to rectangular
2cos theta= sintheta+ r

convert the following rectangular equation to polar
3x=y²

Remember that $\displaystyle \begin{align*} x = r\cos{\theta} \implies \cos{\theta} &= \frac{x}{r}, y = r\sin{\theta} \implies \sin{\theta} = \frac{y}{r}, r^2 = x^2 + y^2 \end{align*}$ , then

$\displaystyle \begin{align*} 2\cos{\theta} &= \sin{\theta} + r \\ \frac{2x}{r} &= \frac{y}{r} + r \\ 2x &= y + r^2 \\ 2x &= y + x^2 + y^2 \\ 0 &= x^2 - 2x + y^2 + y \\ (-1)^2 + \left(\frac{1}{2}\right)^2 &= x^2 - 2x + (-1)^2 + y^2 + y + \left(\frac{1}{2}\right)^2 \\ \frac{5}{4} &= \left(x - 1\right)^2 + \left(y + \frac{1}{2}\right)^2 \end{align*}$

What kind of a relation is this?

Follow a similar process for the second question.

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