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

1. INQUIRY ACTIVITY SUMMARY: 
   

   
   

   1.     An identity is a proven fact and formula that are always true. The Pythagorean Theorem is an identity because it has been proven that two sides of a right triangle squared is equal to the hypotenuse squared(a^ + b^2= c^2). Using the variables x,y, and r, the the pythagorean theorem is x^2+ y^2 = r^2. Seeing that (x/r)^2 + (y/r)^2=1, and the ratio of x/r is cosine and y/r is sine signifies that sin2x+cos2x=1 relates to both trig functions (sin and cos). A right triangle on the first quadrant of the Unit Circle also has the coordinates sin and cos so using the Pythaorean theorem you can use that to obtain sin2x+cos2x=1. Using the ordered pair for 30* is (rad3/2,1/2), so (rad3/2)^2 + (1/2)^2 = 1 shows that this identity is true.

   
   

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1. INQUIRY ACTIVITY REFLECTION
   
   
   
   1. “The connections that I see between Units N, O, P, and Q so far are…” The Unit Circle and its ratios play a vital part in the Pythagorean Identities. the Pythagorean Theorem plays together with the Pythagorean Identites and the ratios from the Unit Circle together with their trig ratios.
   
   
   
   
   
   2. “If I had to describe trigonometry in THREE words, they would be…”ratios, Unit Circle, Pythagorean Theorem (these can be 3 separate words or 3 words that go together… ideally I would like 3 separate words though)