I/D #1:Unit Q-Pythagorian Identities

Inquiry Activity Summary

1. Where does where sin2x+cos2x=1 come from to begin with?

• The equation sin2x+cos2x=1 derives from the Pythagorean Theorem. As you can see if you were to replace both sine and cosine with the variables with variables you can get the regular a^2+b^2=c^2 which is the equation that we usually use to find a side of a right side triangle. Or then we can also replace it with x^2+y^2=r^2 which is the equation that we have been using to solve some triangles in unit P, but for this unit we want the "r^2" to be equal to 1. To be able to do that you would have to divide the equation by "r" which will give you ratios from the unit circle that you can be able to change to cosine, sine, or tangent depending on the ratio. So you will get (x/r)^2+(y/r)^2=1, the (x/r) is the ratio for sine and (y/r) would be the ratio for cosine. The new equation that you would get would be sin2x+cos2x=1. 
• 30 degrees= (radical 3 over 2, 1/2)
• 45 degrees= (radical 2 over 2, radical 2 over 2)
• 60 degrees= (1/2, radical 3 over 2)

2. Show and explain how to derive the two remaining Pythagorean Identities from sin2x+cos2x=1.

 

Inquiry Activity Reflection

1.The connections that I see between Units N, O, P, and Q so far are that all of the units so far is at all of the sections begin to piece back to the unit circle from it being the angles or the ratios or the plotting points. Then there's the use of equations except for the fact that we just begin to change variables around to fit he concept. 

2. If I had to describe trigonometry in THREE words, they would be PRACTICE MAKES PERFECT.