First we have to remember that the Pythagorean theorem is an identity, and what this means is that no matter what the formula will always be true. When we use x, y, and r means that we are basing things on the unit circle. for this reason the identity is equal to 1, because we are basing ourselves on how the unit circle always equals to one. we know that the ratio of cosine in the unit circle is x/r and the ratio of sine in the unit circle is y/r. What i notice is that everything of this is related to the unit circle and the ratios in it. for that reason is that the identity of sin2x+cos2x=1.

Show and explain how to derive the two remaining Pythagorean Identities from sin2x+cos2x=1

One of the first things that you should do is to decide which trig function you want to derive. if it's sin firs you have to move sine to the other side and do the same with the one ending up with 1 - cos2x = sin2x. and you do the same thing for cosine ending up with 1 - sin2x = cos2x.

**The connections that I see between Units N, O, P, and Q so far are**that all the trigonometric functions in the end connect with each other. They all come back to its origins which for us was the unit circle.

If I had to describe trigonometry in THREE words, they would be... Relationship, Angles, Confusing