8-4 Relationships Among Functions

This week we learned some relationships among functions here are some of the relationships that will help you. You can also find these on page 317:


Pythagorean Relationships:
sin^2 θ + cos^2 θ =1
1 + tan^2 θ = sec^2 θ
1 + cot^2 θ = csc^2 θ

Reciprocal Relationships:
csc θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ

Steps: followed loosely
1. Algebra
2. Identities-try Pythagorean Theorem, then move everything to sin and cos if that will help
3. Algebra
4. Continue with 1-3 to end of problem

*TRIG FUNCTIONS CAN’T CANCEL IN EQUATIONS, YOU HAVE TO GER THEM ON ONE SIDE AND FACTOR IT OUT*

Example 1: cos^2 θ + sin^2 θ

You don’t need to use algebra all you need to do is look at you Pythagorean Relationships and you see sin^2 θ + cos^2 θ =1

So you know your answer is 1.

Example 2: (secx-1) (secx+1)

Step one is to look for algebra and you see that you can Foil it out so after you Foil it you get: sec^2x + secx – secx – 1, and too of your secx’s cancel so then it looks like this: sec^2x – 1.

Now you look at your Pythagorean Relationships and you see 1+ tan^2x = sec^2x

So your answer would be tan^2x.

--Danielle :)