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Error comments on Stupid Questions February 2015 - Less Wrong Discussion
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Describing sine and cosine this way, instead of in terms of triangles, suddenly makes their behavior feel much more intuitive to me; on par with the way complex numbers in general suddenly made sense when someone here described multiplication by i as a rotation.
Thanks.
More elementarily: cos x and sin x are the x and y coordinates of the point on the unit circle at an angle x anticlockwise from the positive x-axis. (I think this is the correct version of the "triangles" definitions.)
If you don't rotate, the cosine is still there; only the sine is zero. So, in some sense, cosine is more fundamental; it was there before the rotation.