Trig Graphing Quiz

The voltage used by most households can be modeled by a sine function. The maximum voltage is 120 volts, and there are 60 cycles every second. Which equation best represents the value of the voltage as it flows through the electric wires, where t is time in seconds?

• V = 120sin(t)

• V = 120sin(60t)

• V = 120sin(60πt)

• V = 120sin(120πt)

Which function's graph has a period of 8 and reaches a maximum height of 1 if at least one full period is graphed?

• y = -4cos(π/4 x) - 3

• y = -4cos(π/4 x) + 5

• y = -4cos(8x) - 3

• y = -4cos(8x) + 5

The function f(x) = a cos(bx) + c is plotted on the graph shown below.

• a = 2, b = 6, c = 3

• a = 2, b = 3, c = 1

• a = 4, b = 6, c = -5

• a = 4, b = π/3, c = -3

The depth of the water at a marker 20 feet from the shore in a bay is depicted in the graph below. If the depth, d, is measured in feet and time, t, is measured in hours since midnight, what is an equation for the depth of the water at the marker?

• d = 5cos(2π/6 t) + 9

• d = 9cos(2π/6 t) + 5

• d = 9sin(2π/6 t) + 5

• d = 5sin(2π/6 t) + 9

The temperature, in degrees Fahrenheit, in Times Square during a day in August can be predicted by the function T(x) = 8sin(0.3x - 3) + 74, where x is the number of hours after midnight. According to this model, the predicted temperature, to the nearest degree Fahrenheit, at 7 P.M. is

• 68

• 74

• 77

• 81

The Ferris wheel at the landmark Navy Pier in Chicago takes 7 minutes to make one full rotation. The height, H, in feet, above the ground of one of the six-person cars can be modeled by H(t) = 70sin(2π/7 (t - 1.75)) + 80, where t is time, in minutes. Using H(t) for one full rotation, this car's minimum height, in feet, is

• 150

• 70

• 10

• 0

The average monthly temperature, T(m), in degrees Fahrenheit, over a 12 month period, can be modeled by T(m) = −23cos(π/6 m) + 56, where m is in months. What is the range of temperatures, in degrees Fahrenheit, of this function?

• [−23,23]

• [33,79]

• [−23,56]

• [−79,33]

The hours of daylight, y, in Utica in days, x, from January 1, 2013 can be modeled by the equation y = 3.06sin(0.017x − 1.40) + 12.23. How many hours of daylight, to the nearest tenth, does this model predict for February 14, 2013?

• 9.4

• 10.4

• 12.1

• 12.2

The depth of the water, d(t), in feet, on a given day at Thunder Bay, t hours after midnight is modeled by d(t) = 5sin(π/6 (t − 5)) + 7. Which statement about the Thunder Bay tide is false?

• Low tide occurred at 2 a.m.

• The maximum depth of the water was 12 feet.

• The water depth at 9 a.m. was approximately 11 feet.

• The difference in water depth between high tide and low tide is 14 feet.

A pendulum's swing, S(t), in centimeters, at a given time t, in seconds, can be modeled by the equation S(t) = 15cos(πt/4). What is the amplitude of the pendulum's swing?

• 15 cm

• π/4 cm

• π cm

• 60 cm