Precalculus Chapter 5.1 Using Fundamental Identities

Objectives: Recognize and write trig identities Use trig identities to evaluate, simplify, and rewrite trig expressions

Fundamental Trigonometric Identities

uu

uu

uu

cot1tan

sec1cos

csc1sin

uu

uu

uu

tan1cot

cos1sec

sin1csc

Fundamental Trigonometric Identities

uuu

uuu

sincoscot

cossintan

uu

uu

uu

22

22

22

csccot1

sectan1

1cossin

Co functions

uuuu

uuuu

uuuu

sec2

csc;csc2

sec

tan2

cot;cot2

tan

sin2

cos;cos2

sin

Even or Odd functions

uuuu

Odd

csc)csc(sinsin

uuuu

Even

sec)sec(cos)cos(

uuuu

Odd

cot)cot(tan)tan(

Using identities to evaluate a function

Given:Find the values of all 6 trig functions.

3sec ; tan 02and

Simplifying a Trig Expression

Simplify: tan cscx x

Simplifying a Trig Expression

Simplify: 21 cos cscx x

Simplifying a Trig Expression

Simplify: seccsc

Simplifying a Trig Expression

Simplify: 2cos

1 sinyy

Simplifying a Trig Expression

Simplify: 2tan

sec 1x

x

Simplifying a Trig Expression

Simplify 2 2 2sec tan secx x x

Simplifying a Trig Expression

Simplify xxx sincossin 2

Simplifying a Trig Expression

Factor and Simplify

sec2 2sec 1

Simplifying a Trig Expression

Simplify

cosu1 sinu

1 sinu

cosu

2secu

Simplifying a Trig Expression

Simplify the trigonometric expression:sec tan csc 1x x x

Homework

5.1 pg. 345: 5, 15-67 odd

Precalculus 5.1 Using Fundamental Identities 20