8-4

So, today we are going to learn about relationships in trig functions. This is one of those things that will get easier and easier as you do it. There are steps to these kinds of problems although you follow them very loosely. They are:

1. Do as much basic algebra as you can.

2. Identity: try to use one of your Pythagorean identities if you can, if not, change everything to sine and cosine.

3. Do algebra again.

4. Follow all the steps again.

Some things that you will need to know are:

Pythagorean Identities:

• sin^2x+cos^2x=1
• 1+tan^2x=sec^2x
• 1+cot^2x=csc^2x

Formulas for changing to Sine and Cosine:

• cscx=1/sinx
• tanx=sinx/cosx
• cotx=cosx/sinx
• secx=1/cosx

Now for the example:

Sec^2x-1

Step 1: there is no possible algebra that can be done to this problem

Step 2: You can use the pythagorean identity "1+tan^2x=sec^2x". Solve for Sec^2x- 1 which would give you tan^2x.

Your answer would be tan^2x!!!

I hope you learned something! OH, and i know it's depressing that this isn't colorful, but I'm super tired, so next time guys :)))

Carlaaaay!