73 Periodic Graphs and Amplitude

copy 2008 Roy L Gover(wwwmrgovercom)

Learning GoalsbullUnderstand period and amplitude of a Trigonometric functionbullIntroduce real world applications of periodic graphs

Important IdeaPeriod and amplitude are important in describing the nature of many real world phenomenon such as light waves sound waves and radio waves

Larger PeriodSmaller Frequency

Important Idea

Radio Visible X-Ray

Smaller PeriodGreater Frequency

Important Idea

Radio Visible X-Ray

Important Idea

Radio Waves

Important Idea

Medicine

Important Idea

Ocean Tides

Definition

A complete waveform of a periodic function with no repeats is a cycle

Important IdeaA cycle may be measured in different ways but for a given function the period will be the same

Period

Definition

The Period is the time required for the function to repeat

t

( )f t

Go to Sketchpad

Important IdeaPeriod and amplitude are important in describing the nature of many real world phenomenon such as light waves sound waves and radio waves

Larger PeriodSmaller Frequency

Important Idea

Radio Visible X-Ray

Smaller PeriodGreater Frequency

Important Idea

Radio Visible X-Ray

Important Idea

Radio Waves

Important Idea

Medicine

Important Idea

Ocean Tides

Definition

A complete waveform of a periodic function with no repeats is a cycle

Important IdeaA cycle may be measured in different ways but for a given function the period will be the same

Period

Definition

The Period is the time required for the function to repeat

t

( )f t

Go to Sketchpad

Larger PeriodSmaller Frequency

Important Idea

Radio Visible X-Ray

Smaller PeriodGreater Frequency

Important Idea

Radio Visible X-Ray

Important Idea

Radio Waves

Important Idea

Medicine

Important Idea

Ocean Tides

Definition

A complete waveform of a periodic function with no repeats is a cycle

Important IdeaA cycle may be measured in different ways but for a given function the period will be the same

Period

Definition

The Period is the time required for the function to repeat

t

( )f t

Go to Sketchpad

Smaller PeriodGreater Frequency

Important Idea

Radio Visible X-Ray

Important Idea

Radio Waves

Important Idea

Medicine

Important Idea

Ocean Tides

Definition

A complete waveform of a periodic function with no repeats is a cycle

Important IdeaA cycle may be measured in different ways but for a given function the period will be the same

Period

Definition

The Period is the time required for the function to repeat

t

( )f t

Go to Sketchpad

Important Idea

Radio Waves

Important Idea

Medicine

Important Idea

Ocean Tides

Definition

A complete waveform of a periodic function with no repeats is a cycle

Important IdeaA cycle may be measured in different ways but for a given function the period will be the same

Period

Definition

The Period is the time required for the function to repeat

t

( )f t

Go to Sketchpad

Important Idea

Medicine

Important Idea

Ocean Tides

Definition

A complete waveform of a periodic function with no repeats is a cycle

Important IdeaA cycle may be measured in different ways but for a given function the period will be the same

Period

Definition

The Period is the time required for the function to repeat

t

( )f t

Go to Sketchpad

Important Idea

Ocean Tides

Definition

A complete waveform of a periodic function with no repeats is a cycle

Important IdeaA cycle may be measured in different ways but for a given function the period will be the same

Period

Definition

The Period is the time required for the function to repeat

t

( )f t

Go to Sketchpad

Definition

A complete waveform of a periodic function with no repeats is a cycle

Important IdeaA cycle may be measured in different ways but for a given function the period will be the same

Period

Definition

The Period is the time required for the function to repeat

t

( )f t

Go to Sketchpad

Important IdeaA cycle may be measured in different ways but for a given function the period will be the same

Period

Definition

The Period is the time required for the function to repeat

t

( )f t

Go to Sketchpad

Definition

The Period is the time required for the function to repeat

t

( )f t

Go to Sketchpad

Definition

Frequency (in cycles per second) is the reciprocal of the period

Start Movie

Start Movie

Try ThisbullWhat are your observations about the movement of the bridge

bullWhat do you think is the connection between this bridge and todayrsquos lesson

Important Idea

The x-axis is now the t-axis (time) The y-axis is now the f (t) axis

t

( )f t

Important IdeaFor the trigonometric functions

( ) sinf t bt( ) cosg t bt

or

The constant b changes the period

DefinitionThe trigonometric functions

( ) sinf t bt( ) cosg t bt

have periods (repeat) every 2

b

radians

ExampleWhat is the period of

( ) sinf t t

02

Period=2

21

ExampleWhat is the period of

( ) sin(2 )g t t0 2

2

2

Period=

ExampleWhat is the period of

( ) sin(5 )h t t

Period=2

45

0 4 8

Important Idea

( ) sin( )f t x

( ) sin(2 )g t t

( ) sin(5 )h t t0 2 4

As b gets small period gets large

Try ThisWhat is the period (how often does the function repeat) ( ) cosp t t

22

1

0 2 4

Try ThisWhat is the period (how often does the function repeat) ( ) cos12p t t

2167

12

0 167

Try This

Which is the graph of ( ) sin(4 )f t t 0

red2

Try ThisWhat is the equation of the function graphed in blue( ) sin(2 )f t t

02

Important IdeaThe trigonometric function( ) tanf t bt

has a period (repeats) every b

radians

t

( )f t

b

b

ExampleDetermine how often the function repeats (period) ( ) tan(2 )k t t

( ) tan3

tj t

Try ThisDetermine how often the function repeats (period)

( ) tan6

tp t

1

6b 6 period=

Try ThisUsing your calculator graph

1 tany t

2 tan6

ty

Compare and contrast

DefinitionAmplitude is where is the distance from the middle to the top and

aa

ais the distance from the middle to the bottom

aa

Geom Sketchpad

Important Idea

The x-axis is now the t-axis (time) The y-axis is now the f (t) axis

t

( )f t

Important IdeaFor the trigonometric functions

( ) sinf t bt( ) cosg t bt

or

The constant b changes the period

DefinitionThe trigonometric functions

( ) sinf t bt( ) cosg t bt

have periods (repeat) every 2

b

radians

ExampleWhat is the period of

( ) sinf t t

02

Period=2

21

ExampleWhat is the period of

( ) sin(2 )g t t0 2

2

2

Period=

ExampleWhat is the period of

( ) sin(5 )h t t

Period=2

45

0 4 8

Important Idea

( ) sin( )f t x

( ) sin(2 )g t t

( ) sin(5 )h t t0 2 4

As b gets small period gets large

Try ThisWhat is the period (how often does the function repeat) ( ) cosp t t

22

1

0 2 4

Try ThisWhat is the period (how often does the function repeat) ( ) cos12p t t

2167

12

0 167

Try This

Which is the graph of ( ) sin(4 )f t t 0

red2

Try ThisWhat is the equation of the function graphed in blue( ) sin(2 )f t t

02

Important IdeaThe trigonometric function( ) tanf t bt

has a period (repeats) every b

radians

t

( )f t

b

b

ExampleDetermine how often the function repeats (period) ( ) tan(2 )k t t

( ) tan3

tj t

Try ThisDetermine how often the function repeats (period)

( ) tan6

tp t

1

6b 6 period=

Try ThisUsing your calculator graph

1 tany t

2 tan6

ty

Compare and contrast

DefinitionAmplitude is where is the distance from the middle to the top and

aa

ais the distance from the middle to the bottom

aa

Geom Sketchpad

Important IdeaFor the trigonometric functions

( ) sinf t bt( ) cosg t bt

or

The constant b changes the period

DefinitionThe trigonometric functions

( ) sinf t bt( ) cosg t bt

have periods (repeat) every 2

b

radians

ExampleWhat is the period of

( ) sinf t t

02

Period=2

21

ExampleWhat is the period of

( ) sin(2 )g t t0 2

2

2

Period=

ExampleWhat is the period of

( ) sin(5 )h t t

Period=2

45

0 4 8

Important Idea

( ) sin( )f t x

( ) sin(2 )g t t

( ) sin(5 )h t t0 2 4

As b gets small period gets large

Try ThisWhat is the period (how often does the function repeat) ( ) cosp t t

22

1

0 2 4

Try ThisWhat is the period (how often does the function repeat) ( ) cos12p t t

2167

12

0 167

Try This

Which is the graph of ( ) sin(4 )f t t 0

red2

Try ThisWhat is the equation of the function graphed in blue( ) sin(2 )f t t

02

Important IdeaThe trigonometric function( ) tanf t bt

has a period (repeats) every b

radians

t

( )f t

b

b

ExampleDetermine how often the function repeats (period) ( ) tan(2 )k t t

( ) tan3

tj t

Try ThisDetermine how often the function repeats (period)

( ) tan6

tp t

1

6b 6 period=

Try ThisUsing your calculator graph

1 tany t

2 tan6

ty

Compare and contrast

DefinitionAmplitude is where is the distance from the middle to the top and

aa

ais the distance from the middle to the bottom

aa

Geom Sketchpad

DefinitionThe trigonometric functions

( ) sinf t bt( ) cosg t bt

have periods (repeat) every 2

b

radians

ExampleWhat is the period of

( ) sinf t t

02

Period=2

21

ExampleWhat is the period of

( ) sin(2 )g t t0 2

2

2

Period=

ExampleWhat is the period of

( ) sin(5 )h t t

Period=2

45

0 4 8

Important Idea

( ) sin( )f t x

( ) sin(2 )g t t

( ) sin(5 )h t t0 2 4

As b gets small period gets large

Try ThisWhat is the period (how often does the function repeat) ( ) cosp t t

22

1

0 2 4

Try ThisWhat is the period (how often does the function repeat) ( ) cos12p t t

2167

12

0 167

Try This

Which is the graph of ( ) sin(4 )f t t 0

red2

Try ThisWhat is the equation of the function graphed in blue( ) sin(2 )f t t

02

Important IdeaThe trigonometric function( ) tanf t bt

has a period (repeats) every b

radians

t

( )f t

b

b

ExampleDetermine how often the function repeats (period) ( ) tan(2 )k t t

( ) tan3

tj t

Try ThisDetermine how often the function repeats (period)

( ) tan6

tp t

1

6b 6 period=

Try ThisUsing your calculator graph

1 tany t

2 tan6

ty

Compare and contrast

DefinitionAmplitude is where is the distance from the middle to the top and

aa

ais the distance from the middle to the bottom

aa

Geom Sketchpad

ExampleWhat is the period of

( ) sinf t t

02

Period=2

21

ExampleWhat is the period of

( ) sin(2 )g t t0 2

2

2

Period=

ExampleWhat is the period of

( ) sin(5 )h t t

Period=2

45

0 4 8

Important Idea

( ) sin( )f t x

( ) sin(2 )g t t

( ) sin(5 )h t t0 2 4

As b gets small period gets large

Try ThisWhat is the period (how often does the function repeat) ( ) cosp t t

22

1

0 2 4

Try ThisWhat is the period (how often does the function repeat) ( ) cos12p t t

2167

12

0 167

Try This

Which is the graph of ( ) sin(4 )f t t 0

red2

Try ThisWhat is the equation of the function graphed in blue( ) sin(2 )f t t

02

Important IdeaThe trigonometric function( ) tanf t bt

has a period (repeats) every b

radians

t

( )f t

b

b

ExampleDetermine how often the function repeats (period) ( ) tan(2 )k t t

( ) tan3

tj t

Try ThisDetermine how often the function repeats (period)

( ) tan6

tp t

1

6b 6 period=

Try ThisUsing your calculator graph

1 tany t

2 tan6

ty

Compare and contrast

DefinitionAmplitude is where is the distance from the middle to the top and

aa

ais the distance from the middle to the bottom

aa

Geom Sketchpad

ExampleWhat is the period of

( ) sin(2 )g t t0 2

2

2

Period=

ExampleWhat is the period of

( ) sin(5 )h t t

Period=2

45

0 4 8

Important Idea

( ) sin( )f t x

( ) sin(2 )g t t

( ) sin(5 )h t t0 2 4

As b gets small period gets large

Try ThisWhat is the period (how often does the function repeat) ( ) cosp t t

22

1

0 2 4

Try ThisWhat is the period (how often does the function repeat) ( ) cos12p t t

2167

12

0 167

Try This

Which is the graph of ( ) sin(4 )f t t 0

red2

Try ThisWhat is the equation of the function graphed in blue( ) sin(2 )f t t

02

Important IdeaThe trigonometric function( ) tanf t bt

has a period (repeats) every b

radians

t

( )f t

b

b

ExampleDetermine how often the function repeats (period) ( ) tan(2 )k t t

( ) tan3

tj t

Try ThisDetermine how often the function repeats (period)

( ) tan6

tp t

1

6b 6 period=

Try ThisUsing your calculator graph

1 tany t

2 tan6

ty

Compare and contrast

DefinitionAmplitude is where is the distance from the middle to the top and

aa

ais the distance from the middle to the bottom

aa

Geom Sketchpad

ExampleWhat is the period of

( ) sin(5 )h t t

Period=2

45

0 4 8

Important Idea

( ) sin( )f t x

( ) sin(2 )g t t

( ) sin(5 )h t t0 2 4

As b gets small period gets large

Try ThisWhat is the period (how often does the function repeat) ( ) cosp t t

22

1

0 2 4

Try ThisWhat is the period (how often does the function repeat) ( ) cos12p t t

2167

12

0 167

Try This

Which is the graph of ( ) sin(4 )f t t 0

red2

Try ThisWhat is the equation of the function graphed in blue( ) sin(2 )f t t

02

Important IdeaThe trigonometric function( ) tanf t bt

has a period (repeats) every b

radians

t

( )f t

b

b

ExampleDetermine how often the function repeats (period) ( ) tan(2 )k t t

( ) tan3

tj t

Try ThisDetermine how often the function repeats (period)

( ) tan6

tp t

1

6b 6 period=

Try ThisUsing your calculator graph

1 tany t

2 tan6

ty

Compare and contrast

DefinitionAmplitude is where is the distance from the middle to the top and

aa

ais the distance from the middle to the bottom

aa

Geom Sketchpad

Important Idea

( ) sin( )f t x

( ) sin(2 )g t t

( ) sin(5 )h t t0 2 4

As b gets small period gets large

Try ThisWhat is the period (how often does the function repeat) ( ) cosp t t

22

1

0 2 4

Try ThisWhat is the period (how often does the function repeat) ( ) cos12p t t

2167

12

0 167

Try This

Which is the graph of ( ) sin(4 )f t t 0

red2

Try ThisWhat is the equation of the function graphed in blue( ) sin(2 )f t t

02

Important IdeaThe trigonometric function( ) tanf t bt

has a period (repeats) every b

radians

t

( )f t

b

b

ExampleDetermine how often the function repeats (period) ( ) tan(2 )k t t

( ) tan3

tj t

Try ThisDetermine how often the function repeats (period)

( ) tan6

tp t

1

6b 6 period=

Try ThisUsing your calculator graph

1 tany t

2 tan6

ty

Compare and contrast

DefinitionAmplitude is where is the distance from the middle to the top and

aa

ais the distance from the middle to the bottom

aa

Geom Sketchpad

Try ThisWhat is the period (how often does the function repeat) ( ) cosp t t

22

1

0 2 4

Try ThisWhat is the period (how often does the function repeat) ( ) cos12p t t

2167

12

0 167

Try This

Which is the graph of ( ) sin(4 )f t t 0

red2

Try ThisWhat is the equation of the function graphed in blue( ) sin(2 )f t t

02

Important IdeaThe trigonometric function( ) tanf t bt

has a period (repeats) every b

radians

t

( )f t

b

b

ExampleDetermine how often the function repeats (period) ( ) tan(2 )k t t

( ) tan3

tj t

Try ThisDetermine how often the function repeats (period)

( ) tan6

tp t

1

6b 6 period=

Try ThisUsing your calculator graph

1 tany t

2 tan6

ty

Compare and contrast

DefinitionAmplitude is where is the distance from the middle to the top and

aa

ais the distance from the middle to the bottom

aa

Geom Sketchpad

Try ThisWhat is the period (how often does the function repeat) ( ) cos12p t t

2167

12

0 167

Try This

Which is the graph of ( ) sin(4 )f t t 0

red2

Try ThisWhat is the equation of the function graphed in blue( ) sin(2 )f t t

02

Important IdeaThe trigonometric function( ) tanf t bt

has a period (repeats) every b

radians

t

( )f t

b

b

ExampleDetermine how often the function repeats (period) ( ) tan(2 )k t t

( ) tan3

tj t

Try ThisDetermine how often the function repeats (period)

( ) tan6

tp t

1

6b 6 period=

Try ThisUsing your calculator graph

1 tany t

2 tan6

ty

Compare and contrast

DefinitionAmplitude is where is the distance from the middle to the top and

aa

ais the distance from the middle to the bottom

aa

Geom Sketchpad

Try This

Which is the graph of ( ) sin(4 )f t t 0

red2

Try ThisWhat is the equation of the function graphed in blue( ) sin(2 )f t t

02

Important IdeaThe trigonometric function( ) tanf t bt

has a period (repeats) every b

radians

t

( )f t

b

b

ExampleDetermine how often the function repeats (period) ( ) tan(2 )k t t

( ) tan3

tj t

Try ThisDetermine how often the function repeats (period)

( ) tan6

tp t

1

6b 6 period=

Try ThisUsing your calculator graph

1 tany t

2 tan6

ty

Compare and contrast

DefinitionAmplitude is where is the distance from the middle to the top and

aa

ais the distance from the middle to the bottom

aa

Geom Sketchpad

Try ThisWhat is the equation of the function graphed in blue( ) sin(2 )f t t

02

Important IdeaThe trigonometric function( ) tanf t bt

has a period (repeats) every b

radians

t

( )f t

b

b

ExampleDetermine how often the function repeats (period) ( ) tan(2 )k t t

( ) tan3

tj t

Try ThisDetermine how often the function repeats (period)

( ) tan6

tp t

1

6b 6 period=

Try ThisUsing your calculator graph

1 tany t

2 tan6

ty

Compare and contrast

DefinitionAmplitude is where is the distance from the middle to the top and

aa

ais the distance from the middle to the bottom

aa

Geom Sketchpad

Important IdeaThe trigonometric function( ) tanf t bt

has a period (repeats) every b

radians

t

( )f t

b

b

ExampleDetermine how often the function repeats (period) ( ) tan(2 )k t t

( ) tan3

tj t

Try ThisDetermine how often the function repeats (period)

( ) tan6

tp t

1

6b 6 period=

Try ThisUsing your calculator graph

1 tany t

2 tan6

ty

Compare and contrast

DefinitionAmplitude is where is the distance from the middle to the top and

aa

ais the distance from the middle to the bottom

aa

Geom Sketchpad

ExampleDetermine how often the function repeats (period) ( ) tan(2 )k t t

( ) tan3

tj t

Try ThisDetermine how often the function repeats (period)

( ) tan6

tp t

1

6b 6 period=

Try ThisUsing your calculator graph

1 tany t

2 tan6

ty

Compare and contrast

DefinitionAmplitude is where is the distance from the middle to the top and

aa

ais the distance from the middle to the bottom

aa

Geom Sketchpad

Try ThisDetermine how often the function repeats (period)

( ) tan6

tp t

1

6b 6 period=

Try ThisUsing your calculator graph

1 tany t

2 tan6

ty

Compare and contrast

DefinitionAmplitude is where is the distance from the middle to the top and

aa

ais the distance from the middle to the bottom

aa

Geom Sketchpad

Try ThisUsing your calculator graph

1 tany t

2 tan6

ty

Compare and contrast

DefinitionAmplitude is where is the distance from the middle to the top and

aa

ais the distance from the middle to the bottom

aa

Geom Sketchpad

DefinitionAmplitude is where is the distance from the middle to the top and

aa

ais the distance from the middle to the bottom

aa

Geom Sketchpad

Try ThisCompare and Contrast( ) 5sinf t t( ) 2sing t t

Try ThisWhat is the amplitude of ( ) 6 tanp t tHint this is a trick question

Important Idea( ) sinf t a bt ( ) cosg t a bt

The constant a controls the amplitude (vertical stretch) The constant b controls the horizontal stretch Amplitude is

Period is

a2

b

Try ThisFind the amplitude and period for ( ) sinf t t

Amplitude=1 Period =2

Try ThisFind the amplitude and period for ( ) 3cos2f t t

Amplitude=3 Period =

Try ThisFind the amplitude and period for ( ) 3cos2f t t

Amplitude=3 Period =

Try ThisFind the amplitude and period for ( ) 3tan(5 )f t t

Amplitude None Period=2

Example

For what value(s) of t between is

sin 2 1t 0 1t

Example

For what value(s) of t between [0 ] is

cos2 0t 2

Example

For what value(s) of t between [0 ] is

cos3 0t 2

Try This

For what value(s) of t between [0 ] is

sin3 0t

03

t t

Try This

For what value(s) of t between [01] is

sin3 0t 1 2

0 13 3

t

Lesson ClosePeriod and amplitude will be important when we study modeling and simple harmonic motion in section 84

• PowerPoint Presentation
• Important Idea
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Definition
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Try This
• Slide 14
• Slide 15
• Slide 16
• Example
• Slide 18
• Slide 19
• Slide 20
• Try This
• Slide 22
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• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Lesson Close

Try ThisWhat is the amplitude of ( ) 6 tanp t tHint this is a trick question

Important Idea( ) sinf t a bt ( ) cosg t a bt

The constant a controls the amplitude (vertical stretch) The constant b controls the horizontal stretch Amplitude is

Period is

a2

b

Try ThisFind the amplitude and period for ( ) sinf t t

Amplitude=1 Period =2

Try ThisFind the amplitude and period for ( ) 3cos2f t t

Amplitude=3 Period =

Try ThisFind the amplitude and period for ( ) 3cos2f t t

Amplitude=3 Period =

Try ThisFind the amplitude and period for ( ) 3tan(5 )f t t

Amplitude None Period=2

Example

For what value(s) of t between is

sin 2 1t 0 1t

Example

For what value(s) of t between [0 ] is

cos2 0t 2

Example

For what value(s) of t between [0 ] is

cos3 0t 2

Try This

For what value(s) of t between [0 ] is

sin3 0t

03

t t

Try This

For what value(s) of t between [01] is

sin3 0t 1 2

0 13 3

t

Lesson ClosePeriod and amplitude will be important when we study modeling and simple harmonic motion in section 84

• PowerPoint Presentation
• Important Idea
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Definition
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Try This
• Slide 14
• Slide 15
• Slide 16
• Example
• Slide 18
• Slide 19
• Slide 20
• Try This
• Slide 22
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• Slide 40
• Slide 41
• Lesson Close

Important Idea( ) sinf t a bt ( ) cosg t a bt

The constant a controls the amplitude (vertical stretch) The constant b controls the horizontal stretch Amplitude is

Period is

a2

b

Try ThisFind the amplitude and period for ( ) sinf t t

Amplitude=1 Period =2

Try ThisFind the amplitude and period for ( ) 3cos2f t t

Amplitude=3 Period =

Try ThisFind the amplitude and period for ( ) 3cos2f t t

Amplitude=3 Period =

Try ThisFind the amplitude and period for ( ) 3tan(5 )f t t

Amplitude None Period=2

Example

For what value(s) of t between is

sin 2 1t 0 1t

Example

For what value(s) of t between [0 ] is

cos2 0t 2

Example

For what value(s) of t between [0 ] is

cos3 0t 2

Try This

For what value(s) of t between [0 ] is

sin3 0t

03

t t

Try This

For what value(s) of t between [01] is

sin3 0t 1 2

0 13 3

t

Lesson ClosePeriod and amplitude will be important when we study modeling and simple harmonic motion in section 84

• PowerPoint Presentation
• Important Idea
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Definition
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Try This
• Slide 14
• Slide 15
• Slide 16
• Example
• Slide 18
• Slide 19
• Slide 20
• Try This
• Slide 22
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• Lesson Close

Try ThisFind the amplitude and period for ( ) sinf t t

Amplitude=1 Period =2

Try ThisFind the amplitude and period for ( ) 3cos2f t t

Amplitude=3 Period =

Try ThisFind the amplitude and period for ( ) 3cos2f t t

Amplitude=3 Period =

Try ThisFind the amplitude and period for ( ) 3tan(5 )f t t

Amplitude None Period=2

Example

For what value(s) of t between is

sin 2 1t 0 1t

Example

For what value(s) of t between [0 ] is

cos2 0t 2

Example

For what value(s) of t between [0 ] is

cos3 0t 2

Try This

For what value(s) of t between [0 ] is

sin3 0t

03

t t

Try This

For what value(s) of t between [01] is

sin3 0t 1 2

0 13 3

t

Lesson ClosePeriod and amplitude will be important when we study modeling and simple harmonic motion in section 84

• PowerPoint Presentation
• Important Idea
• Slide 3
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• Definition
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• Try This
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• Example
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• Try This
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• Lesson Close

Try ThisFind the amplitude and period for ( ) 3cos2f t t

Amplitude=3 Period =

Try ThisFind the amplitude and period for ( ) 3cos2f t t

Amplitude=3 Period =

Try ThisFind the amplitude and period for ( ) 3tan(5 )f t t

Amplitude None Period=2

Example

For what value(s) of t between is

sin 2 1t 0 1t

Example

For what value(s) of t between [0 ] is

cos2 0t 2

Example

For what value(s) of t between [0 ] is

cos3 0t 2

Try This

For what value(s) of t between [0 ] is

sin3 0t

03

t t

Try This

For what value(s) of t between [01] is

sin3 0t 1 2

0 13 3

t

Lesson ClosePeriod and amplitude will be important when we study modeling and simple harmonic motion in section 84

• PowerPoint Presentation
• Important Idea
• Slide 3
• Slide 4
• Slide 5
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• Slide 7
• Definition
• Slide 9
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• Try This
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• Example
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• Try This
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• Lesson Close

Try ThisFind the amplitude and period for ( ) 3cos2f t t

Amplitude=3 Period =

Try ThisFind the amplitude and period for ( ) 3tan(5 )f t t

Amplitude None Period=2

Example

For what value(s) of t between is

sin 2 1t 0 1t

Example

For what value(s) of t between [0 ] is

cos2 0t 2

Example

For what value(s) of t between [0 ] is

cos3 0t 2

Try This

For what value(s) of t between [0 ] is

sin3 0t

03

t t

Try This

For what value(s) of t between [01] is

sin3 0t 1 2

0 13 3

t

Lesson ClosePeriod and amplitude will be important when we study modeling and simple harmonic motion in section 84

• PowerPoint Presentation
• Important Idea
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Definition
• Slide 9
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• Try This
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• Example
• Slide 18
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• Try This
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• Lesson Close

Try ThisFind the amplitude and period for ( ) 3tan(5 )f t t

Amplitude None Period=2

Example

For what value(s) of t between is

sin 2 1t 0 1t

Example

For what value(s) of t between [0 ] is

cos2 0t 2

Example

For what value(s) of t between [0 ] is

cos3 0t 2

Try This

For what value(s) of t between [0 ] is

sin3 0t

03

t t

Try This

For what value(s) of t between [01] is

sin3 0t 1 2

0 13 3

t

Lesson ClosePeriod and amplitude will be important when we study modeling and simple harmonic motion in section 84

• PowerPoint Presentation
• Important Idea
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Definition
• Slide 9
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• Try This
• Slide 14
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• Slide 16
• Example
• Slide 18
• Slide 19
• Slide 20
• Try This
• Slide 22
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• Lesson Close

Example

For what value(s) of t between is

sin 2 1t 0 1t

Example

For what value(s) of t between [0 ] is

cos2 0t 2

Example

For what value(s) of t between [0 ] is

cos3 0t 2

Try This

For what value(s) of t between [0 ] is

sin3 0t

03

t t

Try This

For what value(s) of t between [01] is

sin3 0t 1 2

0 13 3

t

Lesson ClosePeriod and amplitude will be important when we study modeling and simple harmonic motion in section 84

• PowerPoint Presentation
• Important Idea
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Definition
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Try This
• Slide 14
• Slide 15
• Slide 16
• Example
• Slide 18
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• Slide 20
• Try This
• Slide 22
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• Lesson Close

Example

For what value(s) of t between [0 ] is

cos2 0t 2

Example

For what value(s) of t between [0 ] is

cos3 0t 2

Try This

For what value(s) of t between [0 ] is

sin3 0t

03

t t

Try This

For what value(s) of t between [01] is

sin3 0t 1 2

0 13 3

t

Lesson ClosePeriod and amplitude will be important when we study modeling and simple harmonic motion in section 84

• PowerPoint Presentation
• Important Idea
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Definition
• Slide 9
• Slide 10
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• Slide 12
• Try This
• Slide 14
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• Example
• Slide 18
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• Try This
• Slide 22
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• Lesson Close

Example

For what value(s) of t between [0 ] is

cos3 0t 2

Try This

For what value(s) of t between [0 ] is

sin3 0t

03

t t

Try This

For what value(s) of t between [01] is

sin3 0t 1 2

0 13 3

t

Lesson ClosePeriod and amplitude will be important when we study modeling and simple harmonic motion in section 84

• PowerPoint Presentation
• Important Idea
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Definition
• Slide 9
• Slide 10
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• Slide 12
• Try This
• Slide 14
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• Slide 16
• Example
• Slide 18
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• Try This
• Slide 22
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• Lesson Close

Try This

For what value(s) of t between [0 ] is

sin3 0t

03

t t

Try This

For what value(s) of t between [01] is

sin3 0t 1 2

0 13 3

t

Lesson ClosePeriod and amplitude will be important when we study modeling and simple harmonic motion in section 84

• PowerPoint Presentation
• Important Idea
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Definition
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Try This
• Slide 14
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• Slide 16
• Example
• Slide 18
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• Try This
• Slide 22
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• Slide 40
• Slide 41
• Lesson Close

Try This

For what value(s) of t between [01] is

sin3 0t 1 2

0 13 3

t

Lesson ClosePeriod and amplitude will be important when we study modeling and simple harmonic motion in section 84

• PowerPoint Presentation
• Important Idea
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Definition
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Try This
• Slide 14
• Slide 15
• Slide 16
• Example
• Slide 18
• Slide 19
• Slide 20
• Try This
• Slide 22
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• Slide 36
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• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Lesson Close

Lesson ClosePeriod and amplitude will be important when we study modeling and simple harmonic motion in section 84

• PowerPoint Presentation
• Important Idea
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Definition
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Try This
• Slide 14
• Slide 15
• Slide 16
• Example
• Slide 18
• Slide 19
• Slide 20
• Try This
• Slide 22
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• Lesson Close