Section 5.1 Simplifying More Trig Expressions Fundamental Trigonometric Identities: Reciprocal...

Section 5.1

Simplifying More Trig Expressions

Fundamental Trigonometric Identities:Reciprocal Identities:

1sin

csc

1cos

sec

1tan

cot

1csc

sin

1

seccos

1

cottan

Quotient Identities:

sintan

cos

coscot

sin

Pythagorean Identities:2 2sin cos 1 2 21 tan sec 2 21 cot csc

Cofunction Identities:

sin cos2

cos sin2

tan cot2

cot tan2

sec csc2

csc sec2

Even / Odd Identities:

sin( ) sin

csc( ) csc

sec( ) sec

cos( ) cos

tan( ) tan

cot( ) cot

Trig Identities

•Any relationship that is true for all values of the variable for which each side is defined is called an identity. 

•We can use trig identities to simplify trig expressions, prove other identities and solve more complex trig equations.

Strategies for Simplifying Trig Expressions:

1.

2.

3.

4.

5.

We can factor trigonometric expressions, too!

Ex 1: Factor each trig expression

A. B. C. 2sec 1 24 tan tan 3 2csc 2csc 3

sin cotx x

Ex 2: Use trig identities to simplify

2 2csc 1 cosx x

Ex 3: Use trig identities to simplify

Ex 4: Simplify by factoring:

2cos 4

cos 2

x

x

Ex 5: Use trig identities to simplify

2sin cos sinx x x

Ex 6: Simplify by adding the fractions first:

1 1

sec 1 sec 1x x

Ex 7: Simplify by factoring

4 2csc 2csc 1

Ex 8: Simplify by adding the fractions first:

sec tan

cos cot

x x

x x

HomeworkPage 379

(2, 27-36 multiples of 3, 45-53 odd, 61, 64, 65)