Why the name Pythagorean Identity is appropriate?

Why the name Pythagorean Identity is appropriate? 

The Pythagorean Identities are trigonometric functions that are made using the Pythagorean Theorem.   The name Pythagorean Theorem is appropriate because the function is based on the Pythagorean Theorem.

The Pythagorean Theorem is the equation a^2+b^2=c^2, where a and b are the legs of a right triangle and c is the hypotenuse. 

Similarly, in a unit circle, there are right triangles. The radius of a unit circle is always 1 and it is the hypotenuse of the right triangle created by an angle. The legs of the triangle are the  length of the y and x axis. The length of the y axis is called sine and the length of the x axis is called cosine.

Now, the Pythagorean Theorem can be used to make an equation for the right triangle in the unit circle. 

cos^2θ+sin^2θ=1^2

or 

cos^2θ+sin^2θ=1

This equation if called Pythagorean Identity number 1.When this 

equation is solved in terms of one of the legs, it leads to 

Pythagorean Identity #2 and  #3. 

#2.cos^2θ+sin^2θ = 1        

cos^2θ  cos^2θ  cos^2θ
1+tan^2θ=sec^2θ

#3.cos^2θ+sin^2θ = 1        

sin^2θ   sin^2θ     sin^2θ
cot^2θ+1=csc^2θ