Advanced Algebra 2
5.5 (Part 3) Graphs of Sine & Cosine
Name: __________________________________ Pd___
1. Find the equation of each graph.
a.
b
Period:________
Amplitude:_______
Period:________
Amplitude:_______
Vertical Translation:_______
Phase Shift: ________
Vertical Translation:_______
Phase Shift: ________
Equation: ______________________________________
Equation: ______________________________________
c.
d.
Period:________
Amplitude:_______
Period:________
Amplitude:_______
Vertical Translation:_______
Phase Shift: ________
Vertical Translation:_______
Phase Shift: ________
Equation: ______________________________________
e.
Equation: ______________________________________
f.
Period:________
Amplitude:_______
Period:________
Amplitude:_______
Vertical Translation:_______
Phase Shift: ________
Vertical Translation:_______
Phase Shift: ________
Equation: ______________________________________
Equation: ______________________________________
g.
h..
Period:________
Amplitude:_______
Period:________
Amplitude:_______
Vertical Translation:_______
Phase Shift: ________
Vertical Translation:_______
Phase Shift: ________
Equation: ______________________________________
Equation: ______________________________________
2. A rancher buys a herd of cattle knowing that the size of the herd will vary sinusoidally with time. The size
of the herd is increasing and reaches a maximum of 1650 cattle 2 years after the rancher buys the herd. The
size of the herd then decreases to a minimum of 1300 cattle 9 years after the rancher buys the herd.
a.
Write a model expressing the size of the herd in terms of the number of years the rancher has owned
the herd.
b.
Use your model to predict the size of the herd in 10 years.
c. Use your model to predict how long it will take for the herd to reach 1400 cattle for the first time.
3. Mulder and Scully find a creature from an alien planet. Its body temperature is varying sinusoidally with
time. 35 minutes after they start timing, it reaches a high of 120°F. 20 minutes after that it reaches its low of
104°F. This pattern then continues.
a. Write an equation expressing temperature in terms of minutes since they started timing.
b. Use your equation to find the alien's temperature when they started timing.
c. Find the first 3 times after they started timing at which the alien's temperature was 114°F.
1. Possible Solutions – Remember there is more than one correct answer
2
𝜋
3
2
a. 𝑦 = 3 cos ( (𝑥 − ))
b. 𝑦 = 3 cos(4𝑥)
1
c. 𝑦 = −4 sin (16 𝑥)
1
1
d. 𝑦 = 6 cos (12 (𝑥 − 6𝜋)) − 2 or 𝑦 = 6 sin (12 𝑥) − 2
1
e. 𝑦 = 2 sin (10 𝑥) − 4
2
f. 𝑦 = 2.5 cos (3 (𝑥 + 𝜋)) + 4.5
𝜋
g. 𝑦 = 3.5 cos (5 (𝑥 − 1)) + 5.5
h. 𝑦 = 5 cos(10𝑥)
𝜋
2. a. 𝑦 = 175 cos (7 (𝑥 − 2)) + 1475
b. 1317 cattle
c. Possible answers: 6.5 years, 11.5 years
𝜋
3. a. 𝑦 = 8 cos ( (𝑥 − 35)) + 112
20
b. 117.7°
c. at minute 3.4, 26.6, and 43.4