Identities/Formulas

8-4: Relationships among functions

---> In order to find relationships among functions you must use identities. <---

Identities are formulas that are used to show how trig functions can be used with other trig functions and how they may relate. You use these formulas by following the steps and if possible using old algebra to end up with a simplified version of your answer.

You will sometimes be asked to just simplify, in which you simplify the equation down to the smallest possible answer you can get it.

You will also be asked to prove, which means you only have to show the steps of how to get the answer they've already given you. These are the steps that you should follow.

1.Algebra

2.Identities-try pythagorean first. If it doesnt work, try to change all to sin and cos

3.Algebra

4.Identities and so on repeat until all the way simplified

Identities:
Pythagorean
sin^2@+cos^22=1 1+tan^2@=sec^2@

1+cot^2@=csc^2@

Reciprical
csc@=1/sin@ secf=1/cos@

cot@=1/tan@

Cofunction
sin@=cos(90-@) cos@sin(90-@)
tan@=cot(90-@) cot@=tan(90-@)
sec@=csc(90-@) csc@=sec(90-@)

Ex1
sec^2@-1
This goes with pythagorean formula. Formula states that 1+tan^2@=sec^2@
Therefore this equation is simplified to tan^2@