8-4

This week we learned more of chapter 8. In section 8-4, we talked about pythagorean identities. It looked pretty easy, but once you have to start doing it on your own, it gets more difficult and takes a lot of practice. Before you can start working any problems, you have to learn these pythagorean identities:

1- cos^2 theta = sin^2 theta
csc^2x-1=cot^2x
1-sin^2theta=cos^2theta
sec^2x-1= tan ^2x
sin^2 theta-1=-cos^2theta
sec^2x-tan^2x= 1
cos^2theta-1- -sin^2theta
1- csc^2x=-cot^2x
csc^2x-cot^2x=1
1- sec^2x= -tan^2x
cot^2-csc^2x=-1
tan^2x-sec^2x=-1
tanx= sinx/cosx
cotx=cosx/sinx

When doing these types of problems, all you are basically doing is replacing and simplifying. There isn't much math involved.

There are 5 steps you follow to get the answer to your problem:
1. see if there are any pythagorean identities
2. if not, change everything to either sin, cos, or tan.
3. use algebra and simplify
4. see if there are any pythagorean identities
5. algebra

Some of the steps repeat and sometimes you won't use them all. It all depends on the problem.

ex 1: tanx - cosx
a. the pythagorean identity that goes with tanx is sinx/cosx.
sinx/cosx - cosx
b. the next step you will use is algebra. you multiply the two fractions and cosx cancels out leaving you with sinx.

sinx is your answer.

The problems vary a lot and there are many different ways to do them, but if you practice them and learn the identities, it makes it much easier. This section becomes one of the easiest if you do these types of problems enough.