Something for homework

Hi, to you all, well not really just Mr. Schnat
but you know what I mean :)

Today's question is : Why is the name Pythagorean identity appropriate ?

So, to start we need to know the three Pythagorean identities. 

1. Sin^2(x)+cos^2(x)=1 
2. Tan^2(x)+1= Sec^2(x)
3. 1+ Cot^2(X)=Csc^2 (x)

In these pythagorean identities as you see above,we can use number one to show why pythagorean identities is an appropriate name. 

In the Pythagorean theorem we use : A^2+ B^2= C^2
in the pythagorean identity we just simply substitute the sin and cos value in the A and B value.

For the more visual people here you go :
Pythagorean THEOREM  :    A^2   +  B^2         = C^2
Pythagorean IDENTITY  : Sin^2(x) + Cos^2(x) = 1

This makes sense because when we did the unit circle we learned that the radius otherwise known as C^2 will always equal 1. 

This is also shown in my diagram below . 

From this circle we also learned that sin and cos are the "legs" of out triangle. 

For example :

Because no matter what you do the bases, will always be bases and the radius will always be one the pythagorean identity is an appropriate name because connected to the pythagorean theorem.