- #1

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If you have [itex] r = 2\sin(2\theta) [/itex], how would you convert it to rectangular form? I tried doing this:

[itex] \sin(2\theta) = 2\sin\theta\cos\theta [/itex] which means [itex] r = 4\sin\theta\cos\theta [/itex]. Then I know that [itex] r^{2} = x^{2} + y^{2} [/itex]. We know that [itex] x = r\cos\theta, y = r\sin\theta [/itex]. But then I have a circular argument, where I end up with [itex] y^{2} = y^{2} [/itex]. This means that I have to use another conversion factor. Should I use [itex] \sin\theta = \frac{y}{r} [/itex]?

Thanks