8-4 Review

Things you should know:

• Do all the possible algebra in the problem first.
• After you do everything possible, you should use the Pythagorean identities.
• After you do that you should move everything to sin and cos.
• After that you should do algebra again.
• Once you do all of those steps, you repeat steps 1-3 until the problem is simplified

• Pythagorean Identities:

1. sin^2x + cos^2x = 1
2. 1 + tan^2x = sec^2x
3. 1 + cot^2x = csc^2x

• Changing to sin to cos:

1. cscx = 1/sinx
2. tanx = sinx/cosx
3. cotx = cosx/sinx
4. secx = 1/cosx

Example 1: cos^2x - 1

• You can not do any algebra in this problem.
• If you noticed, this problem is part of your Pythagorean identities
• Since we know sin^2x + cos^2x = 1 then we know cos^2x - 1 = sin^2x.
• Final answer: sin^2x.

Example 2: 1 + cot^2x

• This is the same thing as the last example.
• You can not do any algebra in this problem.
• This problem is part of your Pythagorean identities.
• 1 + cot^2x = csc^2x
• Final answer: csc^2x

-Amber :)