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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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up vote 2 down vote accepted

Hint: The variables are connected by $$ x=r\cos \theta,\quad y=r\sin\theta. $$

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Wow! So I multiply by cos on both sides which turns (r)(cos) to x... and then to get y I multiply sin on both sides... If only I knew those formulas before all this stressing! Thank you so much!! – derekds Apr 28 '12 at 9:04
@derekds, You're very welcome. But you should be able to understand where these formulas come from (i.e., how the Cartesian coordinates are connected to the polar ones). – Artem Apr 28 '12 at 9:06
@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
@Artem I understand where they came from now :) On the right triangle, r is the hypotenuse so cos(θ) = x/r, and sin(θ) = y/r. I'm going to have an edge for the next lesson :) Thanks once again! – derekds Apr 28 '12 at 9:18
@J.M. Thanks :D – derekds Apr 28 '12 at 9:20

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