I/D #3: Unit Q Concept 1: Pythagorean Identities

Inquiry Activity Summary:
We can refer back o our knowledge of the Unit Circle and the Pythagorean Theorem in order to find out the derivation of sin^2x+cos^2x=1. Identities, in math, are proven facts or formulas that are always true. For example, the Pythagorean Theorem is an identity because it is always true. The following image shows and explains how the Unit Circle and the Pythagorean Theorem go together to derive the ratio identity.

We can reverse the process and figure out how to derive Pythagorean identities by using a ratio identity. The following image shows that process using Cosecant and Cotangent:

Inquiry Activity Reflection:
The connections that I see between Units N, O, P, and Q so far are that there are constant references back to the Unit Circle and everything ties in together.
If I had to describe trigonometry in THREE words, they would be challenging, time-consuming, and connected.