Verifying Pythagorean Identity
in the Unit Circle
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Let P(x,y) be a point in quadrant one on the unit circle x2 + y2 = 1. 
Let point O be the origin (0,0).

•  Draw .  Let be the angle formed by and the positive portion of the x-axis.

•  Draw the perpendicular from P to meet the x-axis at point M.

•  State the ratio in terms of .

•  State the ratio in terms of  .

•  State the coordinates of point P in terms of .

•  Substitute your coordinates into the unit circle to verify one of the Pythagorean Identities.

•  Choose P in a different quadrant and repeat the process.  Does the identity continue to be true?