I/D #3 Unit Q Pythagorean Derivations

1. Where does where sin^2x+cos^2x=1 come from to begin with (think Unit Circle!). You should be referring to Unit Circle ratios and the Pythagorean Theorem in your explanation.

Sin^2x +cos^2x=1 comes from the Pythagorean Theorem. Since Sine is equal to y over r and that is eqaul to y^2. Cosine is equal to x over r, which in referring to the Pythagorean Theorem is eqaul to x^2. When you put this together you have x/r^2 + y/r^2 = 1 or sin^2x + cos^2x = 1.

When deriving the two remaining Pythagorean Theorems you have Tan^2theta +1 = Sec^2theta and 1 + Cot^2theta = Cosecant^2theta. For the first one you have tanx= sinx/cosx then you multiply tanx by tanx=sinx/cosx times sinx/cosx you will be left with Tan^2x = Sin^2x/Cos^2x. For the second one you will do the same but have One/tan and one/sin to work with instead of the other two.

2. The connections that I see between Units N, O, P, and Q so far are…

The connections that I see so far are that the unit circle expands so much farther than I thought. I see that the ratios of Sin,Cos, and Tan can be used in many numerous equations across the unit of trigonometry.

3. If I had to describe trigonometry in THREE words, they would be…

Difficult and Tedious