I understand that the period for sine and cosine functions are theta (in radians) + 2pi.

But if you have a point on the unit circle in the first quadrant, and you drew a line parallel to the x-axis until you reached the unit circle in quadrant 2, wouldn't that be the same y-value, thus the same value for sin theta?

If you repeated the process from the point in quadrant 1 and drew a line parallel to the y-axis until you reached the unit circle in quadrant 4, wouldn't that be the same x-value, thus the same value for cos theta?

I don't understand how this works, if the period is 2pi, then why are there other points on the unit circle that would give the same value for x and y, therefore sine and cosine respectively?

I attached a picture, hopefully that makes my confusion clearer.

Screenshot 2018-01-23 at 14.32.16.jpg

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