Identities

Relationships among formulas are done by using identies. There are 4 different sets of identies in this section but only 3 are really relevent. The three sets of identities most commonly used are recipricol relaionships, pythagorean relationships, and cofuntion relationships. These should be kept handy in order to solve problems.

Recipricol 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

Cofunction 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 (not all steps apply to all problems. This is not an exact model to solve all problems)
1.look for algebra to solve
2.look for identities (try pythagorean first, if that fails try to change everything to sin and cos)
3.look for algebra to solve
4.look for identites (repeat until solved down to simple as can be)

EX 1/cos(90-x)
1. no algebra
2.there is a cofuntion identity 1/sin x
3.there is another for recipricol 1/sinx= csc x
final answer is csc x