Modeling and Interpreting Sine and Cosine Functions

A Ferris wheel has a radius of 10 meters and completes one full rotation every 30 seconds. Write a sine function to model the height of a passenger above the ground as a function of time. What is the maximum height of the passenger?

• 20 meters

• 25 meters

• 30 meters

• 15 meters

The temperature in a city varies throughout the day and can be modeled by a cosine function. If the average temperature is 20°C and it fluctuates 5°C, write the equation for the temperature as a function of time. What is the temperature at noon?

• 15°C

• 10°C

• 20°C

• 25°C

A pendulum swings back and forth, and its motion can be modeled by a sine function. If the pendulum has a maximum displacement of 15 cm and completes a cycle every 4 seconds, write the equation for its displacement over time. What is the displacement at 2 seconds?

• 15 cm

• 5 cm

• 10 cm

• 0 cm

A sound wave can be modeled using a cosine function. If the wave has a frequency of 2 Hz and an amplitude of 3 units, write the equation for the wave. What is the value of the wave at 0.5 seconds?

• 2

• 3

• 4

• 1

A lighthouse beam sweeps in a circular motion, completing one full rotation every 10 seconds. If the beam's height above the water can be modeled by a sine function with a maximum height of 20 meters, write the equation for the height of the beam over time. What is the height at 5 seconds?

• 20 meters

• 25 meters

• 15 meters

• 10 meters

A cyclist rides in a circular path with a radius of 5 meters. The height of the cyclist above the ground can be modeled by a cosine function. If the cyclist starts at the highest point, write the equation for the height as a function of time. What is the height after 3 seconds?

• 5.200

• 4.000

• 3.427

• 2.500

The tide in a coastal area can be modeled by a sine function. If the tide rises and falls with a maximum height of 4 meters and a period of 12 hours, write the equation for the tide height as a function of time. What is the tide height at 6 hours?

• 2 meters

• 6 meters

• 4 meters

• 0 meters

A swing moves back and forth in a periodic motion. If the swing reaches a maximum height of 2 meters and completes a cycle every 5 seconds, write the sine function that models the height of the swing over time. What is the height at 1 second?

• 2.5 meters

• 1.1756 meters

• 3.0 meters

• 0.5 meters

A roller coaster follows a path that can be modeled by a cosine function. If the height of the coaster varies between 10 meters and 30 meters, write the equation for the height as a function of time, assuming it completes a loop every 15 seconds. What is the height at 7.5 seconds?

• 25 meters

• 30 meters

• 20 meters

• 15 meters

A clock's minute hand moves in a circular motion, and its position can be modeled by a sine function. If the hand is 6 cm long and completes a full rotation every 60 seconds, write the equation for the vertical position of the tip of the hand. What is the position at 15 seconds?

• 3√2 cm

• 2 cm

• 5 cm

• 4√3 cm