5.1 Using Fundamental Identities

Evaluating trig functionsSimplifying trig expressionsSolve trig equations

Reciprocal Identities

uu

uu

uu

uu

uu

uu

tan

1cot

cos

1sec

sin

1csc

cot

1tan

sec

1cos

csc

1sin

Quotient Identities

u

uu

u

uu

sin

coscot

cos

sintan

Pythagorean identities

uu

uu

uu

22

22

22

csccot1

sectan1

1cossin

Cofunction Identities

uuuu

uuuu

uuuu

sec2

csc csc2

sec

tan2

cot cot2

tan

sin2

cos cos2

sin

Even/Odd identities

uuuu

uuuu

uuuu

cot)cot( tan)tan(

sec)sec( cos)cos(

csc)csc( sin)sin(

Evaluating

Use a given value with an identity to find another trig value

You can also draw a right triangle

Simplifying

Look for a common factor to factor out

Try to write the expression in terms of only 1 trig function

Try to rewrite the expression using only sin and cos

Substitute values from trig identities

Factoring

Rewrite the expression in terms of 1 trig function

Substitute variables for the trig functions to write the expression in polynomial form

Factor the polynomial and then substitute back in the trig function