Can someone walk me through converting polar /rectangular coordinates?

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=y^{2}

Re: Can someone walk me through converting polar /rectangular coordinates?

Quote:

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=y^{2}

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

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

What kind of a relation is this?

Follow a similar process for the second question.