Unit Q 1 Pythagorean Identities Derivation

The formula above comes from the Pythagorean Theorem (y^2+x^2=r^2).  The triangle would look like the picture on the right, which is labeled y, x, and r.  So, if we look at the triangle, we can see that sin^2 in the Pythagorean Identity is y because sin is opp/hyp.  Cos^2 is x on the right triangle because cos is adj/hyp, and 1 is r because r will always equal 1 in this case of the unit circle.

To get the second main (tan^2x+1=sec^2x) identity we do the following below:



















Now to get the 1+cot^2x=csc^2x identity we do the following below: