Review of 8-4

Okay so this week I am going to review section 8-4 which is on the relationship among functions! This was confusing when I first learned it, but it is actually very easy once you remember all the relationships. So first I am going to give you a few notes that you are going to need.

Notes:

• The first thing you do is to do all the possible algebra to the problem.
• Once you do everything possible, you would first try to use your pythagorean identities.
• After that you would move everything to sin and cos.
• The next thing you would do is do algebra again.
• Once you do all of that you keep repeating steps 1 through 3 until your problem is completely simplified.

Okay, so now that you know all that, I am going to give you a few extra things you are going to need to know.

Pythagorean Identities:

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

Changing to Sin and Cos

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

Now that you know everything you need to know, I will work a few examples for you. This is hopefully help you to better understand how to work these problems.

Example 1: 1+tan^2x

• There is no possible algebra that can be done to this problem.
• This problem is one of your pythagorean identities, which is going to make your problem equal to secx^2. That is then going to be your answer.
• So you answer is secx^2.

Example 2: cos^2x+sin^2x

• There is no possible algebra that can be done to this problem.
• You are first going to look for identities, which you can tell that this problem is one of the
• pythagorean identities which means it will equal to 1.
• So you answer is going to be 1.

And that is it for this weeek. See youu next weeek. Byeee.

--Halie!