12X1 T03 02 graphing trig functions (2011)

Graphing Trig Functions

Graphing Trig Functions

1) Sine Curve

Graphing Trig Functions

y1

-1

1) Sine Curve

Graphing Trig Functions

y

x

1

-1

1) Sine Curve

2 3 42

Graphing Trig Functions

y

x

1

-1

1) Sine Curve

2 3 42

Graphing Trig Functions

y

x

1

-1

1) Sine Curve

2 3 42

Graphing Trig Functions

y

x

1

-1

1) Sine Curve

2 3 42

Graphing Trig Functions

y

x

sin xy 1

-1

1) Sine Curve

2 3 42

Graphing Trig Functions

y

x

sin xy 1

-1

1) Sine Curve

2 3 42

x real all:domain

Graphing Trig Functions

y

x

sin xy 1

-1

1) Sine Curve

2 3 42

x real all:domain11-:range y

Graphing Trig Functions

y

x

sin xy

x real all:domain11-:range y

1

-1

1) Sine Curve

2 3 42

period

Graphing Trig Functions

y

x

sin xy

x real all:domain11-:range y

1

-1

1) Sine Curve

2 3 42

In general;

sin cbxay

units 2 periodb

period

Graphing Trig Functions

y

x

sin xy

x real all:domain11-:range y

1

-1

1) Sine Curve

2 3 42

In general;

sin cbxay

units 2 periodb

periodamplitude

Graphing Trig Functions

y

x

sin xy

x real all:domain11-:range y

1

-1

1) Sine Curve

2 3 42

In general;

sin cbxay

units 2 periodb

units amplitude a

periodamplitude

Graphing Trig Functions

y

x

sin xy

x real all:domain11-:range y

1

-1

1) Sine Curve

2 3 42

In general;

sin cbxay

units 2 periodb

units amplitude a

periodamplitude

4period divisions

Graphing Trig Functions

y

x

sin xy

x real all:domain11-:range y

1

-1

1) Sine Curve

2 3 42

In general;

sin cbxay

units 2 periodb

units amplitude a

periodamplitude

4period divisions

left toshift bc

e.g.

29sin5 xy

e.g.

29sin5 xy

units 9

2 period

e.g.

29sin5 xy

units 9

2 period

units 5amplitude

e.g.

29sin5 xy

units 9

2 period

units 5amplitude 18

divisions

e.g.

29sin5 xy

units 9

2 period

units 5amplitude 18

divisions

right to18

shift

e.g.

29sin5 xy

units 9

2 period

units 5amplitude 18

divisions

right to18

shift

y5

-5 9

92

9

x

e.g.

29sin5 xy

units 9

2 period

units 5amplitude 18

divisions

right to18

shift

y5

-5 9

92

9

x

e.g.

29sin5 xy

units 9

2 period

units 5amplitude 18

divisions

right to18

shift

y5

-5 9

92

9

x

e.g.

29sin5 xy

units 9

2 period

units 5amplitude 18

divisions

right to18

shift

y5

-5 9

92

9

x

e.g.

29sin5 xy

units 9

2 period

units 5amplitude 18

divisions

right to18

shift

y5

-5 9

92

9

x

e.g.

29sin5 xy

units 9

2 period

units 5amplitude 18

divisions

right to18

shift

y

29sin5

xy5

-5 9

92

9

x

2) Cosine Curve

2) Cosine Curve cos cbxay

2) Cosine Curve cos cbxay

units 2 periodb

2) Cosine Curve cos cbxay

units 2 periodb

unitsamplitude a

2) Cosine Curve cos cbxay

units 2 periodb

unitsamplitude a4

period divisions

2) Cosine Curve cos cbxay

units 2 periodb

unitsamplitude a4

period divisions

left toshift bc

2) Cosine Curve cos cbxay

units 2 periodb

unitsamplitude a4

period divisions

left toshift bc

e.g. 28

cos4

xy

2) Cosine Curve cos cbxay

units 2 periodb

unitsamplitude a4

period divisions

left toshift bc

e.g. 28

cos4

xy

16

81

2 period

2) Cosine Curve cos cbxay

units 2 periodb

unitsamplitude a4

period divisions

left toshift bc

e.g. 28

cos4

xy

16

81

2 period

4 amplitude

2) Cosine Curve cos cbxay

units 2 periodb

unitsamplitude a4

period divisions

left toshift bc

e.g. 28

cos4

xy

16

81

2 period

4 amplitude

4divisions

2) Cosine Curve cos cbxay

units 2 periodb

unitsamplitude a4

period divisions

left toshift bc

e.g. 28

cos4

xy

16

81

2 period

4 amplitude

4divisions

down upsideup,2left,to8shift

2) Cosine Curve cos cbxay

units 2 periodb

unitsamplitude a4

period divisions

left toshift bc

e.g. 28

cos4

xy

16

81

2 period

4 amplitude

4divisions

down upsideup,2left,to8shift

y

6

-2 8 168 x

2

2) Cosine Curve cos cbxay

units 2 periodb

unitsamplitude a4

period divisions

left toshift bc

e.g. 28

cos4

xy

16

81

2 period

4 amplitude

4divisions

down upsideup,2left,to8shift

y

6

-2 8 168 x

2

2) Cosine Curve cos cbxay

units 2 periodb

unitsamplitude a4

period divisions

left toshift bc

e.g. 28

cos4

xy

16

81

2 period

4 amplitude

4divisions

down upsideup,2left,to8shift

y

6

-2 8 168 x

2

2) Cosine Curve cos cbxay

units 2 periodb

unitsamplitude a4

period divisions

left toshift bc

e.g. 28

cos4

xy

16

81

2 period

4 amplitude

4divisions

down upsideup,2left,to8shift

y

6

-2 8 168 x

2

2) Cosine Curve cos cbxay

units 2 periodb

unitsamplitude a4

period divisions

left toshift bc

e.g. 28

cos4

xy

16

81

2 period

4 amplitude

4divisions

down upsideup,2left,to8shift

y

6

-2 8 168 x

2

2) Cosine Curve cos cbxay

units 2 periodb

unitsamplitude a4

period divisions

left toshift bc

e.g. 28

cos4

xy

16

81

2 period

4 amplitude

4divisions

down upsideup,2left,to8shift

y

6

-2 8 168 x

2

28

cos4

xy

3) Tangent Curve

3) Tangent Curve tan cbxay

3) Tangent Curve tan cbxay

units periodb

3) Tangent Curve tan cbxay

units periodb

2

period divisions

3) Tangent Curve tan cbxay

units periodb

2

period divisions

left toshift bc

3) Tangent Curve tan cbxay

units periodb

2

period divisions

left toshift bc

e.g. 2tan xey

3) Tangent Curve tan cbxay

units periodb

2

period divisions

left toshift bc

e.g. 2tan xey

1

period

3) Tangent Curve tan cbxay

units periodb

2

period divisions

left toshift bc

e.g. 2tan xey

1

period

21 divisions

3) Tangent Curve tan cbxay

units periodb

2

period divisions

left toshift bc

e.g. 2tan xey

1

period

21 divisions

rightto2shift

3) Tangent Curve tan cbxay

units periodb

2

period divisions

left toshift bc

e.g. 2tan xey

1

period

21 divisions

rightto2shift y

1 2 x

3) Tangent Curve tan cbxay

units periodb

2

period divisions

left toshift bc

e.g. 2tan xey

1

period

21 divisions

rightto2shift y

1 2 x

3) Tangent Curve tan cbxay

units periodb

2

period divisions

left toshift bc

e.g. 2tan xey

1

period

21 divisions

rightto2shift y

1 2 x

3) Tangent Curve tan cbxay

units periodb

2

period divisions

left toshift bc

e.g. 2tan xey

1

period

21 divisions

rightto2shift y

1 2 x

2tan xey

3) Tangent Curve tan cbxay

units periodb

2

period divisions

left toshift bc

e.g. 2tan xey

1

period

21 divisions

rightto2shift y

1 2 x

2tan xey

Exercise 14C; 2b, 3b,4b, 5bce, 8, 9, 10b, 13,

15, 16, 17, 20