ID#3: Unit Q Concept 1

Where does sin2x+cos2x=1 come from?
Thinking back to the unit circle, this rule comes from the pythagorean theorem which states "a2+b2=c2".The pythagorean theorem can be written to be x^2+y^2=r^2, this is possible because when we look at a triangle from the unit circle two of its legs are x and y and the hypotenuse is r. But again, when we think back to the unit circle, we want the equation to equal 1, so we divide everything by r to get (x/r)^2 + (y/r)^2 = 1. because we have our identities memorized, we realized that (x/r) and (y/r) have corresponding trig functions. With that being said, we know that Cos= x/r and Sin= y/r. when we plug that back into the equation, we are left with sin2x+cos2x=1. that is why this formula is referred to as the pythagorean identity.