1. An identity is a proven fact that is always true. The Pythagorean Theorem is an identity because it can be proven that a squared plus b squared will equal c squared. In terms of x, y, and r as used in the Unit circle, the Pythagorean theorem is x^2+y^2=r^2. If we try to get the Pythagorean Theorem in terms of x,y, and r equal one, we must divide by r^2. The equation that results is (x/r)^2+(y/r)^2=1. The ratio for cosine on the unit circle is x/y and the ratio for sine on the Unit circle is y/r. If (y/r)^2 is replaced by sine is the equation it will be sin^2 and (x/r)^2 is replaced by cosine it will be cos^2. The equation will end up being sin^2x+cos^2=1.
2. To derive the rest of the remaining identities we must divide different things to get them. We also must use our ratio identities and reciprocal identities to find them.
INQUIRY ACTIVITY REFLECTION:
1.The connections that I see between Units N, O, P, Q are that they all use the Unit Circle as a basis to derive different equations. They also use the Magic Tree to derive certain equations.
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