# How to write parametric equations for a given polar equation?

I'm doing an extra credit problem for math, we haven't learned too much on this topic.

The instructions are: Write parametric equations for the given polar equation.

The problem is: $r = 5\sin\theta$

The answer is: $x = 5(\cos\theta)(\sin\theta)$, $y = 5(\sin^2\theta)$

How do I get there? I thought I'd find the rectangular form and I ended up with the equation: $x^2 + (y - 2.5)^2 = 6.25$ .. but that got me nowhere near the answer.

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Hint: The variables are connected by $$x=r\cos \theta,\quad y=r\sin\theta.$$
@derek: in general, when turning a polar equation into a parametric equation, all you do is replace either of $r$ or $\theta$ in the conversion equations Artem gave, with the polar expression that you have, whichever is easier. –  Ｊ. Ｍ. Apr 28 '12 at 9:14