Topic 3.7: Sinusoidal Function Data Modeling

The figure shows the graph of a trigonometric function f. Which of the following could be an expression for f(x)?

The figure shows the graph of a trigonometric function g. Which of the following could be an expression for g(x)?

• 3cos(x - π/2)

• 3cos(x + π/2)

• 3sin(x - 2π)

• -3sin(x - π)

In a particular city, the amount of daylight hours is modeled by the function D, defined by D(t) = 2.715 cos(0.017t) + 12.250 for 0 ≤ t ≤ 365 days. Based on the model, which of the following is true?

• The maximum amount of daylight hours is 12.250 hours.

• The maximum amount of daylight hours occurs at t = 0 days.

• The minimum amount of daylight hours is 12.250 hours.

• The minimum amount of daylight hours occurs at t = 0 days.

In Myrtle Beach, South Carolina, the height of the tide, in feet (ft), is modeled by the function H, defined by H(t) = 2.1 sin(π/6(t-1)) + 2.6 for 0 ≤ t ≤ 12 hours. Based on this model, which of the following is true?

• The maximum height of the tide is 4.7 feet.

• The maximum height of the tide occurs at t = 1 hours.

• The minimum height of the tide is 2.6 feet.

• The minimum height of the tide occurs at t = 1 hours.

The population of trout in a particular pond can be modeled by the function F, defined by F(t) = 3000 - 1200 cos(2πt) for 0 ≤ t ≤ 10 years. Based on the model, which of the following is true?

• The maximum number of trout is 3000.

• The maximum number of trout occurs at t = 0 years.

• The minimum number of trout is 1200.

• The minimum number of trout occurs at t = 0 years.

The function f is defined by f(x) = a sin(b(x+c)) + d, for constants a, b, c, and d. In the xy-plane, the points (4, 1) and (8, 5) represent a minimum value and a maximum value, respectively, on the graph of f. What are the values of a and d?

• a = 2 and d = 1

• a = 2 and d = 3

• a = 4 and d = 1

• a = 4 and d = 3

The function g is defined by g(x) = a sin(b(x+c)) + d, for constants a, b, c, and d. In the xy-plane, the points (0, -4) and (2π, 8) represent a minimum value and a maximum value, respectively, on the graph of g. What are the values of a and d?

• a = 3 and d = 2

• a = 3 and d = 4

• a = 6 and d = 2

• a = 6 and d = 4

The function h is defined by h(x) = a sin(b(x+c)) + d, for constants a, b, c, and d. In the xy-plane, the points (0, 0) and (2π, 6) represent a minimum value and a maximum value, respectively, on the graph of h. What is the value of b?

• b = 1/2

• b = 1

• b = 2

• b = 4π

The function k is defined by k(x) = a cos(bx) + d, for constants a, b, c, and d. In the xy-plane, the points (0, -4) and (4, 4) represent a minimum value and a maximum value, respectively, on the graph of k. What are the values of a and b?

• a = 4 and b = π/4

• a = 4 and b = 8

• a = -4 and b = π/4

• a = -4 and b = 8