You may exit out of this review and return later without penalty.
Close
Sharing assignments in OpenClass
OpenClass is on a mission to improve & democratize education. Through our platform, educators can share assignments privately or with our entire community to improve accessibility of the best learning resources around the world.
Our assignments guide students through research-backed study sessions to reinforce learning. If this review is relevant to your teachings, feel free to add it to one of your classes!
Our format is simple and engaging: students are asked a retrieval question, then shown corrective feedback and a multiple-choice mastery question to assess their understanding of the material. Assignments adapt to unique student needs and continue to draw questions until a student has demonstrated mastery.
Describe how the amplitude of a sine or cosine function affects its graph. Provide an example with a specific function.
Explain how the period of a sine or cosine function is determined and provide an example with a specific function.
How does a phase shift affect the graph of a sine or cosine function? Provide an example with a specific function.
Describe the effect of a vertical shift on the graph of a sine or cosine function. Provide an example with a specific function.
Explain how the shape of the sine and cosine graphs differ and how they are similar. Provide an example of each.
Describe how the amplitude of the function affects its graph. Provide an example with a specific value for .
Explain how the period of the function changes with different values of . Provide an example with a specific value for .
How does a phase shift affect the graph of the function ? Provide an example with a specific value for .
Compare the graphs of and . How does the phase shift affect the position of the graph?
How does the graph of differ from the graph of ? Discuss the changes in amplitude, period, and phase shift.
A coastal town experiences high tides and low tides every day. The height of the tide can be modeled by the function , where is the height of the tide in feet and is the time in hours. Explain what the amplitude, period, and vertical shift of this function represent in the context of the tides.
A sound wave can be modeled by the function , where is the displacement and is the time in seconds. Determine the frequency and period of this sound wave.
A Ferris wheel has a diameter of 40 meters and completes one full rotation every 5 minutes. If the height of a seat on the Ferris wheel above the ground can be modeled by a cosine function, write the equation for the height in terms of time in minutes, assuming the lowest point of the Ferris wheel is 2 meters above the ground.
A temperature sensor records the temperature in a room over time and finds that it can be modeled by the function , where is the temperature in degrees Celsius and is the time in hours. Describe the temperature fluctuations in the room over a 24-hour period.
A pendulum swings back and forth, and its displacement from the equilibrium position can be modeled by the function , where is the displacement in meters and is the time in seconds. Determine the amplitude, period, and frequency of the pendulum's motion.
A sound wave can be modeled by the function , where is the displacement and is the time in seconds. Determine the frequency and period of this sound wave.
(Student response here)
The frequency of the sound wave is 220 Hz, as the coefficient of in the cosine function is , which corresponds to . Solving for , we get Hz. The period is the reciprocal of the frequency, so seconds.
What is the period of the sound wave in milliseconds?