Unit Q Post # 1

Question: Show and explain how to derive the two remaining Pythagorean Identities from sin^2 x + cos^2 x +1. Make sure to include where sin^2 x + cos^2 x=1 comes from to begin with.

Sin^2 x + cos^2 x=1 comes from the unit circle. First we need to imagine that we have a triangle in the first quadrant. The hypotenuse is equal to one. one of the legs is equal to sine and the other one is equal to cosine. We know that sine is equal to y/r and that cosine is equal to x/r.  Sin^2 x + cos^2 x=1 comes from the unit circle because every triangle that is in the unit circle has a radius of one, so r equals one. This means that we need to look at x^2 + y^2= 1. We know that one of the legs is sine and the other leg is cosine. So if we add sine^2 and cosine^2 together the answer will be one, which is the same as: Sin^2 x + cos^2 x=1

We can get the second Pythagorean Identity by dividing the main identity by cosine, which is shown below.

We can get the third Pythagorean Identity by dividing the main identity by sine, which is shown below.