삼각함수 전체 문제

For the following exercises, construct a sinusoidal function with the provided information, and then solve the equation for the requested values.

Outside temperatures over the course of a day can be modeled as a sinusoidal function. Suppose the temperature varies between $64\text{°F}$ and $86\text{°F}$ during the day and the average daily temperature first occurs at 12 AM. How many hours after midnight does the temperature first reach $70\text{°F?}$

For the following exercises, construct a sinusoidal function with the provided information, and then solve the equation for the requested values.

A Ferris wheel is 20 meters in diameter and boarded from a platform that is 2 meters above the ground. The six o’clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 6 minutes. How much of the ride, in minutes and seconds, is spent higher than 13 meters above the ground?

For the following exercises, construct a sinusoidal function with the provided information, and then solve the equation for the requested values.

A Ferris wheel is 45 meters in diameter and boarded from a platform that is 1 meter above the ground. The six o’clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 10 minutes. How many minutes of the ride are spent higher than 27 meters above the ground? Round to the nearest second

For the following exercises, construct a sinusoidal function with the provided information, and then solve the equation for the requested values.

The sea ice area around the North Pole fluctuates between about 6 million square kilometers on September 1 to 14 million square kilometers on March 1. Assuming a sinusoidal fluctuation, when are there less than 9 million square kilometers of sea ice? Give your answer as a range of dates, to the nearest day.

For the following exercises, construct a sinusoidal function with the provided information, and then solve the equation for the requested values.

The sea ice area around the South Pole fluctuates between about 18 million square kilometers in September to 3 million square kilometers in March. Assuming a sinusoidal fluctuation, when are there more than 15 million square kilometers of sea ice? Give your answer as a range of dates, to the nearest day.

For the following exercises, construct a sinusoidal function with the provided information, and then solve the equation for the requested values.

During a 90-day monsoon season, daily rainfall can be modeled by sinusoidal functions. If the rainfall fluctuates between a low of 2 inches on day 10 and 12 inches on day 55, during what period is daily rainfall more than 10 inches?

For the following exercises, construct a sinusoidal function with the provided information, and then solve the equation for the requested values.

During a 90-day monsoon season, daily rainfall can be modeled by sinusoidal functions. A low of 4 inches of rainfall was recorded on day 30, and overall the average daily rainfall was 8 inches. During what period was daily rainfall less than 5 inches?

For the following exercises, construct a sinusoidal function with the provided information, and then solve the equation for the requested values.

In a certain region, monthly precipitation peaks at 8 inches on June 1 and falls to a low of 1 inch on December 1. Identify the periods when the region is under flood conditions (greater than 7 inches) and drought conditions (less than 2 inches). Give your answer in terms of the nearest day.

For the following exercises, construct a sinusoidal function with the provided information, and then solve the equation for the requested values.

In a certain region, monthly precipitation peaks at 24 inches in September and falls to a low of 4 inches in March. Identify the periods when the region is under flood conditions (greater than 22 inches) and drought conditions (less than 5 inches). Give your answer in terms of the nearest day.

For the following exercises, find the amplitude, period, and frequency of the given function.

The displacement $h(t)$ in centimeters of a mass suspended by a spring is modeled by the function $h(t)=8\sin (6\pi t),$ where $t$ is measured in seconds. Find the amplitude, period, and frequency of this displacement.

For the following exercises, find the amplitude, period, and frequency of the given function.

The displacement $h(t)$ in centimeters of a mass suspended by a spring is modeled by the function $h(t)=11\sin (12\pi t),$ where $t$ is measured in seconds. Find the amplitude, period, and frequency of this displacement.

For the following exercises, find the amplitude, period, and frequency of the given function.

The displacement $h(t)$ in centimeters of a mass suspended by a spring is modeled by the function $h(t)=4\cos \left(\frac{\pi }{2}t\right),$ where $t$ is measured in seconds. Find the amplitude, period, and frequency of this displacement.

For the following exercises, construct an equation that models the described behavior.

The displacement $h(t),$ in centimeters, of a mass suspended by a spring is modeled by the function $h(t)=-5\,\cos (60\pi t),$ where $t$ is measured in seconds. Find the amplitude, period, and frequency of this displacement.

For the following exercises, construct an equation that models the described behavior.

A deer population oscillates 19 above and below average during the year, reaching the lowest value in January. The average population starts at 800 deer and increases by 160 each year. Find a function that models the population, $P,$ in terms of months since January, $t.$

For the following exercises, construct an equation that models the described behavior.

A rabbit population oscillates 15 above and below average during the year, reaching the lowest value in January. The average population starts at 650 rabbits and increases by 110 each year. Find a function that models the population, $P,$ in terms of months since January, $t.$

For the following exercises, construct an equation that models the described behavior.

A muskrat population oscillates 33 above and below average during the year, reaching the lowest value in January. The average population starts at 900 muskrats and increases by 7% each month. Find a function that models the population, $P,$ in terms of months since January, $t.$

For the following exercises, construct an equation that models the described behavior.

A fish population oscillates 40 above and below average during the year, reaching the lowest value in January. The average population starts at 800 fish and increases by 4% each month. Find a function that models the population, $P,$ in terms of months since January, $t.$

For the following exercises, construct an equation that models the described behavior.

A spring attached to the ceiling is pulled 10 cm down from equilibrium and released. The amplitude decreases by 15% each second. The spring oscillates 18 times each second. Find a function that models the distance, $D,$ the end of the spring is from equilibrium in terms of seconds, $t,$ since the spring was released.

For the following exercises, construct an equation that models the described behavior.

A spring attached to the ceiling is pulled 7 cm down from equilibrium and released. The amplitude decreases by 11% each second. The spring oscillates 20 times each second. Find a function that models the distance, $D,$ the end of the spring is from equilibrium in terms of seconds, $t,$ since the spring was released.

For the following exercises, construct an equation that models the described behavior.

A spring attached to the ceiling is pulled 17 cm down from equilibrium and released. After 3 seconds, the amplitude has decreased to 13 cm. The spring oscillates 14 times each second. Find a function that models the distance, $D,$ the end of the spring is from equilibrium in terms of seconds, $t,$ since the spring was released.