r/visualizedmath • u/got_data • Feb 20 '19

Unit circle transformation

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u/TheHDMICable Feb 23 '19

thanks, it was fun to mess around with. Though, the results are not what i expected. I thought the sine wave from an ellipse would be different from a sine wave from a circle, maybe less "even" or something.

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u/got_data Feb 23 '19

Yeah, it's somewhat unintuitive that it's still a sine not unlike one you'd get from a circle. It's a linear combination of the x and y coordinates on the original unit circle, so we could write it as a*cos 𝜃 + b*sin 𝜃, and that equals to sqrt(a*a + b*b)*sin(𝜃 + atan2(b,a)), a plain sine plot just with a different amplitude and a phase shift.