Textbook Question
Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement true.
cot s = 0.5022
Ch. 3 - Radian Measure and The Unit Circle
Lial12th EditionTrigonometryISBN: 9780136552161
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Table of contents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Chapter 4, Problem 3.55
The propeller of a 90-horsepower outboard motor at full throttle rotates at exactly 5000 revolutions per min. Find the angular speed of the propeller in radians per second.
Verified step by step guidance1
Identify the given information: the propeller rotates at 5000 revolutions per minute (rpm). We need to find the angular speed in radians per second.
Recall the relationship between revolutions and radians: one revolution corresponds to \(2\pi\) radians.
Convert revolutions per minute to radians per minute by multiplying the number of revolutions by \(2\pi\): angular speed in radians per minute = \(5000 \times 2\pi\).
Convert the angular speed from radians per minute to radians per second by dividing by 60, since there are 60 seconds in one minute: angular speed in radians per second = \(\frac{5000 \times 2\pi}{60}\).
Simplify the expression if needed to express the angular speed in radians per second.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Angular Speed
Angular speed measures how fast an object rotates or revolves, expressed as the angle covered per unit time. It is commonly measured in radians per second, representing the rate of change of angular displacement.
Conversion from Revolutions per Minute to Radians per Second
To convert revolutions per minute (rpm) to radians per second, multiply by 2π (radians in one revolution) and divide by 60 (seconds in a minute). This conversion translates rotational speed into standard angular velocity units.
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Relationship Between Horsepower and Rotational Speed
While horsepower indicates the power output of the motor, it does not directly affect the angular speed calculation. Understanding this distinction helps focus on rotational speed data (rpm) for angular velocity conversion.
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Related Practice
Textbook Question
Find the angular speed ω for each of the following.
a wind turbine with blades turning at a rate of 15 revolutions per minute
Textbook Question
Find the exact value of s in the given interval that has the given circular function value.
[ π , 3π/2] ; sec s = ―2√3/3
Textbook Question
Work each problem.
Consider each angle in standard position having the given radian measure. In what quadrant does the terminal side lie?
-2
Textbook Question
Work each problem.
Consider each angle in standard position having the given radian measure. In what quadrant does the terminal side lie?
7
2
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Textbook Question
Find the exact value of s in the given interval that has the given circular function value.
[ 0, π/2] ; cos s = √2/2