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
![Proof of Pythagorean Identity-[bci] Hello wonderful mathematicians, today I want to show you some visual proof of pythags ide](https://image.staticox.com/?url=http%3A%2F%2Fpm1.aminoapps.vertvonline.info%2F7348%2Febafefabee53607bcfaba115b26d7127b2d7cc9dr1-1536-2048v2_hq.jpg)
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
![Proof of Pythagorean Identity-[bci] Hello wonderful mathematicians, today I want to show you some visual proof of pythags ide](https://image.staticox.com/?url=http%3A%2F%2Fpm1.aminoapps.vertvonline.info%2F7348%2Fb88f1cc683c4623ac9e58124fb6ef0a5b31ff465r1-1536-2048v2_hq.jpg)
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
![Proof of Pythagorean Identity-[bci] Hello wonderful mathematicians, today I want to show you some visual proof of pythags ide](https://image.staticox.com/?url=http%3A%2F%2Fpm1.aminoapps.vertvonline.info%2F7348%2F5fa8ea6f2baeaeccb87ff5b1cd413c80938f6cdar1-1536-2048v2_hq.jpg)
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
![Proof of Pythagorean Identity-[bci] Hello wonderful mathematicians, today I want to show you some visual proof of pythags ide](https://image.staticox.com/?url=http%3A%2F%2Fpm1.aminoapps.vertvonline.info%2F7348%2F84e2799c658b9cd0e762665c1cac483675800d83r1-1536-2048v2_hq.jpg)
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.
![Proof of Pythagorean Identity-[bci] Hello wonderful mathematicians, today I want to show you some visual proof of pythags ide](https://image.staticox.com/?url=http%3A%2F%2Fpm1.aminoapps.vertvonline.info%2F7348%2Fe21118dd5cb8890d28c5db850c6981e794dd3983r1-1536-2048v2_hq.jpg)
![Proof of Pythagorean Identity-[bci] Hello wonderful mathematicians, today I want to show you some visual proof of pythags ide](https://image.staticox.com/?url=http%3A%2F%2Fpm1.aminoapps.vertvonline.info%2F7348%2F57466f9946f1a57e585037f5d77fd8d44c34548fr1-1536-2048v2_hq.jpg)
Thanks all for reading and hoped you enjoyed the blog! cya next time :)
Comments (4)
Do u know all the algebra properties
Good job. One little thing to point out: you forgot the negative solutions when taking the square root; there should have been a plus/minus in front of each square root.
Right, I assume all square roots have positive and negative answers and forgot the sign. Good pickup! :yum:
Awesome work