I/D3: Unit Q - Pythagorean Identities

INQUIRY ACTIVITY SUMMARY

To find where sin^2x+cos^2x=1 we have to use the pythagorean theorem. X^2+Y^2=R^2. First we need to get R^2 to equal one. we do this by dividing R^2 by itself and divide everything else by R^2. we end up getting X^2/R^2+Y^2/R^2. After, we know that X^2/R^2= Cos^2x because we remember our unit circle. Y^2/R^2= Sin^2x. so we know that Cos^2x+Sin^2x=1.

It's good to know these, but these aren't the only trig functions we need to find. We also need the Tan^2x and the Cot^2x. We divide everything by Cos^2x. We come up with Sin^2x/Cos^2x+1=1/Cos^2x. Sin^2x/Cos^2x=Tan^2x since we remember the trig functions. The final answer will be Tan^2x+1=sec^2x.

To find Cot^2x we divide everything by Sin^2x this time.

We get 1+cos^2x+1/Sin^2x. from this we just simplify and we know that Cos/Sin = Cot because of our unit circle.  And 1/Sin is equal to Csc. so in the end we will get 1+Cot^2x=Csc^2x.

INQUIRY ACTIVITY REFLECTION

1. The connections that i see between Units N, O, P, and Q so far are the use of the trig functions throughout all of these. Also we have kept the unit circle through all of this.

2. If i had to describe trigonometry in THREE words, they would be eww (not sure if thats an acceptable word, if not then 'i don't like it'), difficult and helpful.