Textbook Question
Concept Check Work each problem. Find the equation of the line that passes through the origin and makes a 30° angle with the x-axis.
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3. Unit Circle
Trigonometric Functions on the Unit Circle
Problem 17
Textbook Question
Use the formula ω = θ/t to find the value of the missing variable.
θ = 3.871 radians, t = 21.47 sec
Verified step by step guidance1
Identify the given variables and the formula: angular displacement \(\theta = 3.871\) radians, time \(t = 21.47\) seconds, and the formula for angular velocity \(\omega = \frac{\theta}{t}\).
Substitute the known values into the formula: \(\omega = \frac{3.871}{21.47}\).
Set up the division to calculate \(\omega\), which represents the angular velocity in radians per second.
Perform the division to find the numerical value of \(\omega\) (angular velocity).
Interpret the result as the rate of change of angular displacement with respect to time, measured 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 Displacement (θ)
Angular displacement represents the angle through which an object rotates, measured in radians. It quantifies the change in the angular position of the object and is essential for calculating angular velocity.
Time Interval (t)
Time interval is the duration over which the angular displacement occurs, measured in seconds. It is a key variable in determining the rate of rotation or angular velocity.
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Angular Velocity (ω)
Angular velocity is the rate of change of angular displacement with respect to time, expressed in radians per second. It indicates how fast an object rotates and is calculated using the formula ω = θ / t.
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