I/D 3 Unit Q - Concept 1 Pythagorean Identities

Inquiry Activity Summary

1. An identity is proven facts and formulas that are always true. The Pythagorean Theorem is an identity because it is a proven fact and formula that is always true. When presented with the variables x,y, and r, the Pythagorean Theorem is x^2+y^2=r^2. For example, when you want r to =1 then you would use the Pythagorean theorem (x/r)^2 + (y/r)^2 = 1. The ratio for cosine is (x/y) like what you saw in the Pythagorean theorem above and the ratio for sine is (y/r) like the one from above. With this you notice that the sin and cos ratios equal to 1 and there is a relationship between the Pythagorean theorem and the ratio for trig functions. From this we can conclude that cos^2theta + sin^2theta = 1 This is a Pythagorean identity because it is just a rearrangement of the Pythagorean theorem with trig functions that always works. The example below shows how this identity is true. 

2. Our first Pythagorean identity has secant and tangent. To get our other two Pythagorean identities, we have to divide by either cosine or sine because they are basically the golden ratios that give us the rest of the trig functions and are the easiest to deal with. Basically, with sin or cosine, you can form a trig function from them to make cosecant, secant, tangent, and cotangent. With the 2 examples below, this shows us that our pythagorean identity is truly an identity. 

Inquiry Activity Reflection 
1. "The connections that I see between Units N, O, P, and Q so far are.." trig functions being used for explaining almost every concept and the unit circle being referenced back to as well to explain the triangles and the uses. 

2. " If i had to describe trigonometry in THREE words, they would be..." Too many trigs.