Pythagorean Identities
1. sin2x=cos2x=1 comes from the the unit circle ratios. The sin2x symbolizes sin= y/r and the cos2x symbolizes cos= x/r. Combined together in an equation y/r turns into y, x/r turns into x, and added together it is x+y=r, or x2+y2=r2 which equals to one.
2. sin2x+cos2x=1
If we look back at our Unit Circle we can relate sin equaling to the ratio of y/r; leaving the answer to be y, since the r=1. To continue with the reference of the Unit Circle, cos has the ratio of x/r, leaving us with x. Plugging that into our original equation, we get y^2 + x^2 = 1. Looks similar, it should because it is just like the Pythagorean Theorem of a^2 + b^2 = c^2.
If we look back at our Unit Circle we can relate sin equaling to the ratio of y/r; leaving the answer to be y, since the r=1. To continue with the reference of the Unit Circle, cos has the ratio of x/r, leaving us with x. Plugging that into our original equation, we get y^2 + x^2 = 1. Looks similar, it should because it is just like the Pythagorean Theorem of a^2 + b^2 = c^2.
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