I/D#3: Unit Q - Pythagorean Identities Concept 1: Using fundamental identities to simplify and verify expression (simple, one or two step identities)

1. When you draw a triangle inside a Unit Circle we use Pythagorean Theorem to finding the missing sides. We can use the Pythagorean Theorem to show why it is an identity.

It is referred to a Pythagorean Identity because you are using the Pythagorean Theorem to solve for the triangle and we have our ratios at the end of the equations which show that it is sine and cosine.  

Now if you were to plug in any of the coordinate points from the 30 45 60 degrees reference angles, you will always get answer that is equal to 1. For example:

2. To get the second identity from the Pythagorean Identities you have to take what you got from the first identity which was sin^2x+cos^2x=1 and divide it all by cos^2x. From there you use your ratio and reciprocal identities to find what each divided problem is equal to. And from there you have your tangent and secant identity.

To get the third identity you once again take your first Pythagorean Identity which was sin^2x+cos^2x=1 and divide it all by sin^2x. You then have to multiple divided identities and you use your ratio and reciprocal identities to find what each one equals too and from there you have your final identity that uses cotangent and cosecant