Graphs and Word Problems related to Sine and Cosine

1. The Ferris wheel at an amusement park has a diameter of 40 meters. If it takes 5 minutes to make a full revolution, find the amplitude of the sinusoidal curve modeling the path of a single cart.

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The Ferris wheel at an amusement park has a diameter of 40 meters. If it takes 5 minutes to make a full revolution, write an equation of the sinusoidal curve modeling the path of a single cart.

• y = 40 sin((2π/5)x)

• y = 20 sin((2π/5)x)

• y = 20 sin((2π/5)x)

• y = 20 sin((2π/10)x)

1. The water level in a circular fountain rises and falls periodically with a depth variation of 4 meters. If the period of the water level oscillation is 10 seconds, calculate the amplitude of the sinusoidal function that describes the water level. 

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1. The water level in a circular fountain rises and falls periodically with a depth variation of 4 meters. If the period of the water level oscillation is 10 seconds, Write an equation of the sinusoidal function that describes the water level. 

• y = 4*sin((pi/5)x)

• y = 4*sin((pi/5)x)

• y = 4*sin((pi/10)x)

• y = 4*cos((pi/5)x)

1. At the park, the free fall drop ride follows the function d(t) = 40cos(0.5t) + 50, where d(t) represents the distance in meters at time t in seconds. Find the amplitude and period of the free fall drop ride.

• {'amplitude': 20, 'period': '2π seconds'}
• {'amplitude': 30, 'period': '6π seconds'}
• {'amplitude': 40, 'period': '4π seconds'}
• {'amplitude': 50, 'period': '8π seconds'}

1. The giant slide ride can be represented by the function h(t) = 20cos(0.25t) + 25, where h(t) is the height in meters at time t in seconds. What is the amplitude and period of the giant slide ride?

• {'amplitude': 25, 'period': '10π seconds'}
• {'amplitude': 20, 'period': '4π seconds'}
• {'amplitude': 15, 'period': '6π seconds'}
• {'amplitude': 20, 'period': '8π seconds'}

1. The Tilt-a-Whirl spins riders in circles with a height function h(t) = 12cos(π t) + 18, where t is the time in seconds. Find the amplitude and period of this function.

• Amplitude: 18, Period: 3 seconds
• Amplitude: 6, Period: 4 seconds
• Amplitude: 12, Period: 2 seconds
• Amplitude: 10, Period: 5 seconds

1. The shadow of a 15-meter tall flagpole on the ground varies sinusoidally as the sun moves across the sky during the day. If the maximum shadow length is 16 meters and it repeats every 4 hours, what is the amplitude and period of the shadow function?

• {'amplitude': 12, 'period': 6 hours}

• {'amplitude': 16, 'period': 2 hours}

• {'amplitude': 8, 'period': 4 hours}

• {'amplitude': 4, 'period': 8 hours}

1. The shadow of a 15-meter tall flagpole on the ground varies sinusoidally as the sun moves across the sky during the day. If the maximum shadow length is 16 meters and it repeats every 4 hours, what is sinusoidal function that models this situation?

• y = 8*sin((π/4)x)

• y = 16*sin((π/4)x)

• y = 8*sin((π/2)x)

• y = 8*cos((π/2)x)

Give the equation to the graph on the left.

• y = 3cos(x-pi)

• y = 3sin(x-pi)

• y =-3cos(3x)

• y = 3x - 2