Notes Over 14.5Writing Trigonometric FunctionsWriting Trigonometric FunctionsWrite a function for the sinusoid.

.1 Positive Sine graphNo vertical or

horizontal shifts

xy sin

Amplitude:2

14

1

Period: 1

1

2b 2b2

1

2

1

Notes Over 14.5Writing Trigonometric FunctionsWriting Trigonometric FunctionsWrite a function for the sinusoid.

Negative Cosine graphVertical shift

xy cos

Amplitude: 34

Period:

2

b 2b2

2

3

.2

2,

4,

2

4 22 2

2 1

1

Notes Over 14.5Writing Trigonometric FunctionsWriting Trigonometric FunctionsWrite a function for the sinusoid.

Positive Cosine graphVertical shift

xy cos

Amplitude: 2

1

Period: 2

2

2b b

2

2

.3

5,1

1,2

1 52 2

6 3

3

Notes Over 14.5Writing Trigonometric FunctionsWriting Trigonometric FunctionsWrite a function for the sinusoid.

Negative Sine graphVertical shift

xy sin

Amplitude: 12

Period: 2

2

2b 1b

1

.4

1,

2

3,

2

3

3 12 2

4 2

2

Notes Over 14.5Modeling a SinusoidModeling a Sinusoid5. One complete breathing cycle for a human, consisting of inhaling and exhaling, takes place every 5 seconds on average. If the maximum air flow rate is 0.6 liters per second and varies sinusoidally over time, write a model for the air flow rate r (in liters per second) as a sine function of time t (in seconds).

Positive Sine graph No vertical or horizontal shifts

Amplitude: 6.0

tr sin 6.0

Period: 55

2b

5

2

Notes Over 14.5Modeling a SinusoidModeling a Sinusoid6. A beating heart consists of two phases. In the systolic phase blood rushes through the heart, and in the diastolic phase the heart relaxes. Write a model of the form r =a sin bt for a person whose systolic phase lasts 0.25 second and whose maximum blood flow rate is 0.13 liter per second.

Amplitude: 13.0

tr sin 13.0

Period:225.0 5.0

2b

4 4b

Notes Over 14.5