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Proof of Pythagorean Identity

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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

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

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

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

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
Proof of Pythagorean Identity-[bci] Hello wonderful mathematicians, today I want to show you some visual proof of pythags ide

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

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Comments (4)

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.

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1 Reply 10/16/19
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