Why is the name Pythagorean Identity is appropriate?

We all know that the Pythagorean theorem is written or drawn like this:

a² + b² = c²

^{The Pythagorean Identity used in Trigonometry is very similar to the Pythagorean Theorem. As we learned before, the Pythagorean Identity is:}

 Sin²x+Cos²x=1

Now lets use the same triangle with numbers: 

The Pythagorean Theorem will look like: (3)(3)+(4)(4)=(5)(5)

or 9+16=25

Now using the Pythagorean Identity: 

We have to plug in for Sin²x and Cos²x. So, Sin of x is 3/5 and Cosine of x is 4/5. However, both Sin and Cosine is raised to the second power so we square Sin and Cosine:

(3/5)(3/5)+(4/5)(4/5)

(9/25)+(16/25)=25/25,

and....

25/25=1!

Tada !!

The Pythagorean Identity is an appropriate name for it because when you plug the numbers in the Pythagorean Theorem just how it is formulated (remember Sin and Cosine were raised to the second power, don't forget to raise it to the second power!) you will result in 1, ALL THE TIME! 

If you forget the Pythagorean Identity, remember the Pythagorean theorem and you will succeed in trigonometry!