Pythagorean Identity is an appropriate title for many reasons. Sine and Cosine are the root of all identies and all others come from these two. When defining 'identity' it can be defined as, an equation that is true no matter what values are chosen.
The original Pythagorean Identity is sin^2 θ + cos^2 θ = 1. In the unit circle the hypotenuse is always 1 and the x and y. values are cosine and sine. If you look at the Pythagorean Therom (a^2 + b^2 = c^2) you can see that compared to the Pythagorean Identity it is basically the same thing. Because C is the hypotenuse in the Identity it becomes 1. And cosine and sine are just a and b. Because these two are so related that is why the Pythagorean Identity is an appropriate title. No matter what values you chose it will always be true.
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