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Ch. 1 - Trigonometric Functions
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Lial 12th EditionCh. 1 - Trigonometric Functions문제 127
2장, 문제 127

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?

검증된 단계별 안내
1
Understand the problem: The pulley rotates through an angle of 75° in 1 minute, and we need to find how many full rotations it makes in 1 hour.
Recall that one full rotation corresponds to an angle of 360°. To find the number of rotations, we will convert the total angle rotated in 1 hour into the number of full 360° rotations.
Calculate the total angle rotated in 1 hour. Since 1 hour = 60 minutes, multiply the angle rotated per minute by 60: \(\text{Total angle} = 75^\circ \times 60\).
Find the number of full rotations by dividing the total angle rotated in 1 hour by 360°: \(\text{Number of rotations} = \frac{\text{Total angle}}{360^\circ}\).
Simplify the expression to get the number of rotations the pulley makes in 1 hour.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Angle Measurement in Degrees and Radians

Angles can be measured in degrees or radians, where 360° equals one full rotation. Understanding how to convert between degrees and rotations is essential for solving problems involving rotational motion.
추천 영상:
5:04
Converting between Degrees & Radians

Relationship Between Angular Displacement and Rotations

Angular displacement refers to the angle through which an object rotates. One full rotation corresponds to 360°, so the number of rotations can be found by dividing the total angular displacement by 360°.
추천 영상:
6:50
Convert Equations from Polar to Rectangular

Unit Conversion and Time Scaling

Converting time units (minutes to hours) and scaling angular displacement over time are crucial to determine total rotations over a given period. Multiplying the rotations per minute by the total minutes gives the total rotations.
추천 영상:
06:11
Introduction to the Unit Circle
관련 실천
교과서 질문

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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교과서 질문

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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교과서 질문

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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교과서 질문

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.

676
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