Textbook Question
Determine whether each statement is true or false. See Example 4. csc 20° < csc 30°
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3. Unit Circle
Defining the Unit Circle
Problem 11
Textbook Question
Use the formula ω = θ/t to find the value of the missing variable.
ω = 2π/3 radians per sec, t = 3 sec
Verified step by step guidance1
Identify the given variables and the formula: angular velocity \(\omega = \frac{\theta}{t}\), where \(\omega\) is angular velocity, \(\theta\) is the angular displacement in radians, and \(t\) is the time in seconds.
Substitute the known values into the formula: \(\omega = \frac{2\pi}{3}\) radians per second and \(t = 3\) seconds.
Rewrite the formula to solve for the missing variable \(\theta\): multiply both sides of the equation by \(t\) to get \(\theta = \omega \times t\).
Plug in the known values into the rearranged formula: \(\theta = \left(\frac{2\pi}{3}\right) \times 3\).
Simplify the expression to find \(\theta\), which represents the angular displacement in radians.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Angular Velocity (ω)
Angular velocity measures how fast an object rotates or revolves, expressed in radians per second. It is the rate of change of angular displacement over time, indicating how many radians the object covers each second.
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Angular Displacement (θ)
Angular displacement is the angle through which an object has rotated, measured in radians. It represents the total change in the angular position of the object during a given time interval.
Relationship Between Angular Velocity, Angular Displacement, and Time
The formula ω = θ / t relates angular velocity (ω), angular displacement (θ), and time (t). It shows that angular velocity equals the angular displacement divided by the time taken, allowing calculation of any one variable if the other two are known.
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