INQUIRY ACTIVITY SUMMARY
Pythagorean identities come from the Unit Circle and the Pythagorean Theorem. An Identity is an equation that is true no matter what values are chosen. The Pythagorean Theorem kind of looks like an identity because even if you have 2 sides you can always find the 3rd using the theorem. The Pythagorean theorem is a^2+b^2=c^2 and the Pythagorean identity is cos^2(theta) + sin^2(theta) = 1. but on a unit circle it is x+y=1 we are going to substitute them so a is going to be x, y is b and 1 = r so 1 is c as you can see. r=1 because r is the radius of the circle and the radius of a unit circle is always going to be 1.
\what you can notice about how cosine =x and sine= y that it really does relate because the equation is cos^2(theta) + sin^2(theta) = 1 and you can see cos = x in the equation and sin=y and 1 =1. just like the Pythagorean theorem they are squares and like the unit circle they are x and y. and this is one of the identities.
1. the connection I have seen between Units N,O,P, and Q are that we can find angles on the unit circle and the sides and angles inside triangles that are missing using law of sines and cosines
2) If I had to describe trigonometry in THREE words, they will be hard, understandable, and progressive.