Where does the pythagorean identity sin2 θ + cos2 θ = 1 come from? how 
does it relate to right triangles?

All of the trigonometric functions of an angle θ can be constructed geometrically in terms of a unit circle centered at O. Given that:

Sine function being  
Cosine function being  
 

We will demonstrate the identity above. First of all, we need to square each equation, so:
 



Adding these two equations:



But as shown in the figure, using Pythagorean theorem  is always equal to 1, then:



The relation to right triangles is that:

The hypotenuse is always equal to 1
The opposite side is equal to
The adjacent side is equal to

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