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The Pythagorean Identities (page 1 of 2)
This lesson shows the derivations of the three Pythagorean Identities.
A "derivation" means that we need to create this from scratch - or, at least, from other things that we know.

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Let's start with the Unit Circle:

Zooming in to get a better look, we can label the sides of our right triangle...

By the Pythagorean Theorem, we have that

Since this is a Unit Circle, we have

         

Substituting, gives us


(The first Pythagorean Identity)

Continued on the next page

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