Textbook Question
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. Measuring Angles
Angles in Standard Position
2:08 minutesProblem 4
Textbook Question
Find the angle of least positive measure that is coterminal with each angle. 792°
Verified step by step guidance1
Understand that angles are coterminal if they differ by full rotations of 360°. To find an angle coterminal with 792°, we need to subtract multiples of 360° until the result is between 0° and 360°.
Set up the expression to find the coterminal angle: \(\theta = 792^\circ - 360^\circ \times k\), where \(k\) is an integer chosen so that \(0^\circ \leq \theta < 360^\circ\).
Determine the appropriate value of \(k\) by dividing 792 by 360: \(\frac{792}{360} = 2.2\). Since \(k\) must be an integer, try \(k=2\).
Calculate the coterminal angle using \(k=2\): \(\theta = 792^\circ - 360^\circ \times 2\).
Verify that the resulting angle \(\theta\) is between 0° and 360°, which will be the least positive angle coterminal with 792°.
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2mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Coterminal Angles
Coterminal angles are angles that share the same initial and terminal sides but differ by full rotations of 360°. To find coterminal angles, you add or subtract multiples of 360° from the given angle. This concept helps identify equivalent angles within a standard range.
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Coterminal Angles
Angle Reduction to Least Positive Measure
The least positive measure of an angle is the smallest positive angle coterminal with the given angle, typically between 0° and 360°. To find it, repeatedly subtract 360° from the angle until the result lies within this range, ensuring the angle is positive and minimal.
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Modular Arithmetic in Angle Measurement
Modular arithmetic simplifies angle calculations by treating angles modulo 360°. This means angles differing by multiples of 360° are equivalent, allowing easy computation of coterminal angles using the remainder after division by 360°. It streamlines finding standard angle measures.
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