Notes Over 6.4 Graph Sine, Cosine FunctionsGraph Sine, Cosine Functions

Notes Over 6.4 Graph Sine, Cosine, and Tangent FunctionsGraph Sine, Cosine, and Tangent FunctionsEquation of a Sine Function

xy sin

2

2

3 2

1

1

1Amplitude

2 12

PeriodComplete Cycle

1

22

2

Notes Over 6.4 Graphing a Sine FunctionsGraphing a Sine FunctionsDraw one cycle of the function’s graph.

xy 2sin .1

1

2

2

Amplitude

Period

4

2

4

3

1

1

Notes Over 6.4 Graphing a Sine FunctionsGraphing a Sine FunctionsDraw one cycle of the function’s graph.

xy sin4 .2

4

1

2

Amplitude

Period

2

2

2

3 2

4

4

Notes Over 6.4 Graphing a Sine FunctionsGraphing a Sine FunctionsDraw one cycle of the function’s graph.

xy 4sin3 .3

3

4

2

Amplitude

Period

2

8

4

8

32

3

3

Notes Over 6.4 Graph Sine, Cosine, and Tangent FunctionsGraph Sine, Cosine, and Tangent FunctionsEquation of a Cosine Function

xy cos

2

2

3 2

1

1

1Amplitude

2 12

PeriodComplete Cycle

1

22

2

Notes Over 6.4 Graphing a Cosine FunctionsGraphing a Cosine FunctionsDraw one cycle of the function’s graph.

xy 3cos .4

1

3

2

Amplitude

Period 6

3

2

3

2

1

1

Notes Over 6.4 Graphing a Cosine FunctionsGraphing a Cosine FunctionsDraw one cycle of the function’s graph.

xy 2cos2 .5

2

2

2

Amplitude

Period 4

12

1

4

3 1

2

2

1

Notes Over 6.4 Graphing a Cosine FunctionsGraphing a Cosine FunctionsDraw one cycle of the function’s graph.

xy 2cos3 .6

3

2

2

Amplitude

Period 4

2

4

3

3

3

Notes Over 6.4Translations of Trigonometric GraphsTranslations of Trigonometric GraphsTranslation of a Sine Function

xy sin

2

2

3 2

1

1

1Amplitude

Period2

11

Notes Over 6.4Translations of Trigonometric GraphsTranslations of Trigonometric GraphsTranslation of a Sine Function

siny

2

2

3 2

1

1

1Amplitude

Period2

2

x

2

xx

Notes Over 6.4Graphing a Vertical TranslationGraphing a Vertical TranslationGraph the function.

xy cos2 .7

2

2

3 2

1

3

1Amplitude

Period 2

Translationdown 2

Notes Over 6.4Graphing a Vertical TranslationGraphing a Vertical TranslationGraph the function.

xy sin3 .8

2

2

3 2

4

2

1Amplitude

Period 2

Translationup 3

Notes Over 6.4Graphing a Horizontal TranslationGraphing a Horizontal TranslationGraph the function.

xy sin .9

2

2

3

1

1

Amplitude

Period

Translationright

2

1

2

Notes Over 6.4Graphing a Horizontal TranslationGraphing a Horizontal TranslationGraph the function.

xy cos .10

2

2

3

1

1

Amplitude

Period

Translationleft

2

1

2

Notes Over 6.4Graphing a Horizontal TranslationGraphing a Horizontal TranslationGraph the function.

2cos3 .11

xy

2

2

3

3

3

Amplitude

Period

Translationright

2

3

2

Notes Over 6.4Graphing a ReflectionGraphing a ReflectionGraph the function.

xy cos .12

2

2

3

1

1

2

Amplitude

Period

Reflection over x-axis

1

2

Notes Over 6.4Graphing a ReflectionGraphing a ReflectionGraph the function.

xy sin2

1 .13

2

2

3

1

1

2

Amplitude

Period

Reflection over x-axis

2

1

2

Notes Over 6.4