Download Lesson 5 - Coweta County Schools

Notes Over 14.5
Writing Trigonometric Functions
Write a function for the sinusoid.
1.
1
1
4
1
y  sin 2 x
2
Positive Sine graph
No vertical or
horizontal shifts
1
Amplitude:
2
Period: 1
2
b  2
b
1
Notes Over 14.5
Writing Trigonometric Functions
Write a function for the sinusoid.
 
 ,4 
2 
2.
2

4
 ,2
Negative Cosine graph
Vertical shift
4 2 2
 1
2
2
Amplitude:
y   3 cos2 x  1
3
Period: 
b
2

b2
Notes Over 14.5
Writing Trigonometric Functions
Write a function for the sinusoid.
3.
2
2,1
1
1,5
y  2 cos x  3
Positive Cosine graph
Vertical shift
 1  5  6

 3
2
2
Amplitude:
Period:
2
2
2
b 
b
2
Notes Over 14.5
Writing Trigonometric Functions
Write a function for the sinusoid.
 3 
 ,3 
 2 
4.
 
 ,1
2 
1

2
y   sin x  2
Negative Sine graph
Vertical shift
3 1 4
 2
2
2
1
2
Amplitude:
Period:
2
b
b 1
2
Notes Over 14.5
Modeling a Sinusoid
5. 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: 0.6
Period:
2
r  0.6 sin t
5
2
5 b
5
Notes Over 14.5
Modeling a Sinusoid
6. 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: 0.13
Period:
0.25  2
r  0.13 sin 4 t
2
b
0.5
b  4
Notes Over 14.5