Proof of Pythagorean Identity

Hello wonderful mathematicians, today I want to show you some visual proof of pythags identify.

First, let’s draw out a unit circle such as this

Now let’s draw a line from the origin to the circumference of circle. A unit circle has a radius of 1. And let’s draw a vertical line (y) and a horizontal line (x) that makes a triangle

Now let us the following formulas for how to find x and how to find y in a triangle which are as the following. Note that r stands for the radius and that is equal to one. And also we need to know the Pythagorean Theorem which means x^2 + y^2 is equal to our diagonal which In our case is 1

Now let’s substitute our x and y values into the Pythagorean Theorem and then being out the common factor of r. And since r is equal to one we have now proved that

cos^2(x)+sin^2(x) = 1

Now what we can do with this equation is find that sin and cos is equal too. And this is done by doing simple algebra.

Thanks all for reading and hoped you enjoyed the blog! cya next time :)