Kayla takes a field trip to an amusement park and rides a Ferris wheel. The graph below shows the height, in feet above the ground, of the car over time, t, measured in minutes. What is the amplitude and what does it represent in this context.

The amplitude is 142.5 feet and it represents half the distance between the car's highest point and lowest point.

The amplitude is 285 feet and it represents the distance between the car's highest point and lowest point.

The amplitude is 2 minutes and it represents the time it takes for the Ferris wheel to make a complete cycle.

The amplitude is 305 and it represents how high the Ferris wheel goes.

Sea levels follow a periodic pattern of rise and fall called the tides. The graph below shows the sea level at a certain beach, in feet, over one day, where time t is measured in hours after 12:00 a.m. (midnight) on the first day. What is the period and what does it represent in this context?

The period is 12 hours and it represents the time between consecutive low tides.

The period is 24 hours and it represents the time between consecutive high tides.

The period is 12 hours and it represents the time between sunrise and sunset.

The period is 24 hour and it represents the time in a day.

29. In physics lab, Julia attaches a wireless sensor to one of the spokes of a bicycle wheel spinning freely on its axle. The sensor’s height above the ground, in centimeters, is given by the function $$h\left(t\right)=10.87\sin\left(\frac{\pi}{5}\left(t-7\right)\right)+35.47$$ , where t is time measured in seconds. What is the maximum and what does it represent in this context?

The maximum is 46.34 centimeters and it represents the sensor’s highest point.

The maximum is 24.60 centimeters and it represents the sensor’s lowest point.

The maximum is 35.47 centimeters and it represents the average height of the sensor.

The maximum is 10.87 centimeters and it represents the amplitude of the sensor’s motion.

In physics lab, Madelyn attaches a wireless sensor to one of the spokes of a bicycle wheel spinning freely on its axle. The graph below shows the sensor's height above the ground, in centimeters, over time t, measured in seconds. What is the midline and what does it represent in this context?

The midline is y = 48 centimeters and it represents the sensor's average height off the ground.

The midline is y = 48 centimeters and it represents half the distance between the highest and lowest point.

The midline is y = 6 centimeters and it represents the time it takes for the bicycle wheel to make a full revolution.

The midline is y = 6 centimeters and it represents the number of rotations the wheel makes in one minute.

During a certain time of year, the daily temperature in a certain city, in degrees Fahrenheit follows a periodic pattern. The graph below shows the temperature over two days, where time t is measured in hours after 12:00 a.m. (midnight) on the first day. What is the midline and what does it represent in this context?

The midline is y = 62.5 degrees Fahrenheit and it represents the days’ average temperature.

The midline is y = 75 degrees Fahrenheit and it represents the highest temperature of the day.

The midline is y = 50 degrees Fahrenheit and it represents the lowest temperature of the day.

The midline is y = 100 degrees Fahrenheit and it represents the maximum possible temperature.

Over the course of a full year, the daylight in a certain city follows a periodic pattern given by the function $$D\left(t\right)=153.5\sin\left(\frac{\pi}{6}\left(t-8.5\right)\right)+709.5$$ where D represents the average daylight, in minutes, over the course of twenty-four months, and time t represents the number of months after January 1. What is the midline and what does it represent in this context?

The midline is 709.5 minutes and it represents the years’ average daylight.

The midline is 153.5 minutes and it represents the shortest day of the year.

The midline is 8.5 minutes and it represents the month with the most daylight.

The midline is 709.5 minutes and it represents the maximum daylight in a day.

During a certain time of year, the daily temperature in a certain city, in degrees Fahrenheit follows a periodic pattern, given by the function $$T\left(t\right)=11.5\sin\left(\frac{\pi}{12}\left(t-9.5\right)\right)+60.5$$ , where T represents the temperature and time t is measured in hours after 12:00 a.m. (midnight). What is the amplitude and what does it represent in this context?

The amplitude is 11.5 degrees Fahrenheit and it represents half the difference between the days’ low and high temperatures.

The amplitude is 60.5 degrees Fahrenheit and it represents the average daily temperature.

The amplitude is 11.5 degrees Fahrenheit and it represents the average daily temperature.

The amplitude is 60.5 degrees Fahrenheit and it represents half the difference between the days’ low and high temperatures.

In physics lab, Aaron attaches a wireless sensor to one of the spokes of a bicycle wheel spinning freely on its axle. The sensor’s height above the ground, in centimeters, is given by the function $$h\left(t\right)=22.25\sin\left(\frac{\pi}{5}\left(t-8\right)\right)+48.42$$ , where t is time measured in seconds. What is the amplitude and what does it represent in this context?

The amplitude is 22.25 centimeters and it represents half the distance between the sensor’s highest point and lowest point.

The amplitude is 48.42 centimeters and it represents the average height of the sensor above the ground.

The amplitude is 22.25 centimeters and it represents the total distance traveled by the sensor in one revolution.

The amplitude is 5 centimeters and it represents the time it takes for the wheel to complete one rotation.

Trig Test Review

Authored by Kensley Allen

Mathematics

11th Grade

CCSS covered

Used 4+ times

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34 questions

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find the exact value of tan(-90°).

Undefined

-1

Tags

CCSS.HSF.TF.A.2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find the exact value of sin π in simplest form with a rational denominator.

-1

1/2

Tags

CCSS.HSF.TF.A.2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find the exact value of tan(5π/6) in simplest form with a rational denominator.

-√3/3

√3/3

-1

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find the exact value of cos 135°.

-√2/2

√2/2

1/2

-1

Tags

CCSS.HSF.TF.A.2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find the exact value of sin 330°.

-1/2

1/2

-√3/2

√3/2

Tags

CCSS.HSF.TF.A.2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find the exact value of tan(π/4) in simplest form with a rational denominator.

√2

-1

Tags

CCSS.HSF.TF.A.2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find all angles, 0° ≤ θ < 360°, that solve the following equation. sin θ = -1/2

{θ = 210°, θ = 330°}

{θ = 30°, θ = 150°}

{θ = 120°, θ = 240°}

{θ = 90°, θ = 270°}

Tags

CCSS.HSF.TF.B.7

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Trig Test Review

Find the exact value of tan(-90°).

Find the exact value of sin π in simplest form with a rational denominator.

Find the exact value of tan(5π/6) in simplest form with a rational denominator.

Find the exact value of cos 135°.

Find the exact value of sin 330°.

Find the exact value of tan(π/4) in simplest form with a rational denominator.

Find all angles, 0° ≤ θ < 360°, that solve the following equation. sin θ = -1/2

Find all angles, 0° ≤ θ < 360°, that solve the following equation. cos θ = √3/2

Determine the amplitude of the following graph.

Determine the amplitude of the following graph.

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