I/D #3: Unit Q- Pythagorean Theorem

Inquiry Activity Summary: 
Where does sin^2x+cos^2x=1 come from?

The Pythagorean theorem is derived to become a Pythagorean identity. From the unit circle, the Pythagorean theorem uses "x", "y", and "r" which would become: x^2+y^2=r^2. With this we can perform an operation which allows the equation equal to 1. The operation is to just simply divide r^2 from both sides of the equation which in turn creates (x/r)^2+ (y/r)^2= 1. This then becomes an identity, proven facts and formulas that are always true. From the unit circle we see that cosine equals x/r and sine equals y/r, with these two we can just substitute them into the equation which will then give us the Pythagorean Identity sin^2x+cos^2x=1.

Show and explain how to derive the two remaining Pythagorean Identities from sin^2x+cos^2x=1.

Please look at the pictures below, they already have the descriptions on how I got other two remaining Pythagorean Identities.

Inquiry Activity Reflection:

The connections that I see between Units N, O, P, and Q so far are that they all relate back to the Unit circle. The reason why I say this is because of the fact that when we derive triangles, Heron's Theory, and any of the other equations that we have learned prior to this would reference back to the Unit circle for the legs and hypotenuse which will help us to derive the triangle or theory.

If I had to describe trigonometry in three words, they would be complicated, interesting, and enjoyable. It's complicated because we learn not only the equations and theories given to us but we also learn how it was derived and how it is connected with the real world. It is interesting because prior to learning these mathematical equations and theories you don't really question the math that is going on around you and you especially don't think about how these formulas were derived, so it makes it interesting to see all the math that is around you everyday. And finally it is enjoyable because when you finally understand how to do the problems and understand how you are connected to it, you start to enjoy answering the problem and you begin to see that math isn't as bad as many may think it is.