Identities

During last week we learned mainly about Identities




The most important of identities used are reciprocal relationships, Pythagorean relationships, and co-function relationships. You should either memorize these or make flash cards in order to know them well.

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

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

Co-function Relationships:
sin x=cos(90-0) and cos x=sin(90-0)
tan x=cot(90-0) and cot x=tan(90-0)
sec x=csc(90-0) and csc x=sec(90-0)

Now use steps to solve,some of these steps may not apply to others.
1.look for algebra to solve
2.look for identities – first you should try Pythagorean, if it doesn’t work try to change everything to sin and cos
3.look for algebra to solve
4.look for identities (repeat this until simplified all the way)

Example: (sinx-1)(sinx+1)
Algebra= foiling. (sinx^2-1)
Formula: sin^X = Cos^X