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Ch. 1 - Trigonometric Functions
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161Not the one you use?Change textbook
All textbooksLial 12th EditionCh. 1 - Trigonometric FunctionsProblem 123
Chapter 2, Problem 123

Solve each problem. See Example 6. Revolutions of a Turntable A turntable in a shop makes 45 revolutions per min. How many revolutions does it make per second?

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1
Identify the given information: the turntable makes 45 revolutions per minute (rpm).
Recall the conversion factor between minutes and seconds: 1 minute = 60 seconds.
Set up the conversion to find revolutions per second by dividing the revolutions per minute by the number of seconds in a minute: \(\text{revolutions per second} = \frac{45}{60}\).
Simplify the fraction to express the revolutions per second in simplest form.
Interpret the result as the number of revolutions the turntable makes in one second.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Unit Conversion between Minutes and Seconds

Understanding how to convert time units is essential. Since 1 minute equals 60 seconds, converting revolutions per minute (rpm) to revolutions per second (rps) involves dividing the number of revolutions by 60.
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Revolutions as a Measure of Angular Displacement

A revolution represents one complete turn or rotation. Knowing that revolutions count the number of full rotations helps interpret the problem and convert between different time-based rates of rotation.
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Rate and Proportional Reasoning

The problem involves rates, specifically revolutions per unit time. Applying proportional reasoning allows you to scale the given rate (per minute) to a different time frame (per second) accurately.
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Related Practice
Textbook Question

Solve each problem. See Example 6. Surveying One student in a surveying class measures an angle as 74.25°, while another student measures the same angle as 74° 20' . Find the difference between these measurements, both to the nearest minute and to the nearest hundredth of a degree.

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Textbook Question

Concept Check Sketch each angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, that are coterminal with the given angle. Give the quadrant of each angle, if applicable. ―61 °

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Textbook Question

Solve each problem. See Example 6. Rotating Pulley A pulley rotates through 75° in 1 min. How many rotations does the pulley make in 1 hr?

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Textbook Question

Concept Check Sketch each angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, that are coterminal with the given angle. Give the quadrant of each angle, if applicable. ―90 °

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Textbook Question

Solve each problem. See Example 6. Rotating Airplane Propeller An airplane propeller rotates 1000 times per min. Find the number of degrees that a point on the edge of the propeller will rotate in 2 sec.

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Textbook Question

Concept Check Sketch each angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, that are coterminal with the given angle. Give the quadrant of each angle, if applicable. 90 °

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