5.1 Using Fundamental Identities

5.1 Using Fundamental Identities

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(

Simplify the Trigonometric Identity

Given: y

ysin1

cos2

Simplify the Trigonometric Identity

Given:

y

yyy

yy

sin1sin1

sin1cos

sin1cos

2

2

Simplify the Trigonometric Identity

Given:

yyy

yy

yy

yy

2

2

2

2

sin1sin1cos

sin1sin1

sin1cos

sin1cos

Simplify the Trigonometric Identity

Given:

yyy

yy

yy

yy

2

2

2

2

sin1sin1cos

sin1sin1

sin1cos

sin1cos

yy

yy

22

22

sin1cos

1sincos

Simplify the Trigonometric Identity

Given:

yy

yy

yyy

yy

yy

yy

sin1cos

sin1cos

sin1sin1cos

sin1sin1

sin1cos

sin1cos

2

2

2

2

2

2

Simplify the Trigonometric Identity

Given: 1sec1sec2

xx

Simplify the Trigonometric Identity

Given:

1sec

1sec1sec

1sec1sec2

xxx

xx

Simplify the Trigonometric Identity

Given:

1sec

1sec1sec1sec

1sec1sec2

x

xxx

xx

Evaluate the function

Find the six function valuesGiven:

Cot

Tan

Cos

SinFind

553csc;

23sec

Evaluate the function

Find the six function valuesGiven:

25

552

353

2

35

32

553csc;

23sec

Cot

Tan

Cos

Sin

Find

Simplify a Trigonometric expression

Given: SinCscSin

Simplify a Trigonometric expression

Given:

SinSin

SinSin

SinCscSin

21

Simplify a Trigonometric expression

Given:

22

2

2

1

1

CosSinCosSin

SinSinSin

SinSin

SinSin

SinCscSin

Using Substitution

111

1111

111

1

1

22

22

2

23

23

CscxxCotorCscxCscx

CscxxCscuu

uuu

uuu

CscxuSubstitute

CscxxCscxCsc

Using Substitution

Sin

Sin

SinSin

xx

22

422

422

44

cos116cos1616

)cos4(416

cos2416

cos2;41622

2

22

2

2

2

Using Substitution

Sin

Sin

SinSin

xx

22

422

422

44

cos116cos1616

)cos4(416

cos2416

cos2;41622

2

22

2

2

2

22

21

121

122

2

2

2

2

Cos

Cos

Cos

Cos

Homework

Page 359-361# 1, 17, 27, 37, 47,

53, 57, 65, 77, 87, 93, 107

HomeworkPage 359-361# 10, 26, 36, 48,

54, 58, 68, 78, 88, 94, 120