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

Inquiry Activity Summary:

An identity is a proven fact or formula that is always true. We will be showing you how the pythagorean theorem is an "identity" in my work below:

-Finding: (Sin^2x+Cos^2x=1)
-Pythagorean Theorem: x^2+y^2=r^2
-Sin=y/r; Cos=x/r
-Substitute the trig functions into the pythagorean theorem:
(y/r)^2+ (x/r)^2= 1
-equals the same thing as saying Sin^2x+Cos^2x=1
-We can then check it by lets say, using the 45degree angle in our Unit Circle.
-Coordinates are (rad2/2, rad2/2)
                               x          y
-(rad2/2)^2+ (rad2/2)^2=1
-The radical in rad2 cancels, you square the 2 in the bottom and your left with
-(2/4)+(2/4)=1
-(4/4)=1
-Correct!

Inquiry Activity Reflection:

-The connections that i see between Units N, O, P, and Q so far are that they all have something to do with the unit circle, we have to derive stuff.
-Three words that I would describe trigonometry would be fascinating, hard, but doable.