I/D#3: unit Q-Pythagorean Identities

• First of all an identity is a proven fact that is always true. The Pythagorean Theorem when using x,y and r, it's x^2+y^2=r^2. Then divide everything by r^2 to get one. It will look like this (x^2/r^2)+(y^2/r^2)=1. Since cosine is x/r and sine is y/r. So it will be replace to be cos^2x+sin^2x=1. That's why it's referred to the Pythagorean Theorem. The magic 5 pairs to make an identity true are (1/2,3/2),(2/2,2/2),(3/2,1/2), (0,1) and (1,0). The connection between units N, O, P, and Q so far are the magic 5 pairs or the unit circle and using sin, cos and tan as well as its reciprocals. If I had to describe trigonometry in THREE words, they would be complicated, long and strategically to solve. 
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• For further understanding visit this websites, number three is a video explaining the process:
• 1.http://math.tutorvista.com/geometry/pythagorean-identities.html?view=simple
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• 2.http://www.purplemath.com/modules/idents.htm
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• 3.http://ocw.mit.edu/courses/mathematics/18-01-single-variable-calculus-fall-2006/video-lectures/lecture-27-trig-integrals/