Textbook Question
Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. See Example 5. 26° 30'
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1. Measuring Angles
Angles in Standard Position
2:22 minutesProblem 94
Textbook Question
Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. 8440°
Verified step by step guidance1
Understand that coterminal angles differ by full rotations of 360°. To find an angle coterminal with 8440°, you add or subtract multiples of 360°.
Express the coterminal angle as \(\theta = 8440° - 360° \times k\), where \(k\) is an integer chosen so that \(\theta\) lies between 0° and 360°.
Determine the integer \(k\) by dividing 8440 by 360 and taking the integer part: \(k = \left\lfloor \frac{8440}{360} \right\rfloor\).
Calculate the angle \(\theta\) by subtracting \(360° \times k\) from 8440°, which will give the least positive coterminal angle.
Verify that the resulting angle \(\theta\) is positive and less than 360°, and that it is not equal to the original angle 8440°.
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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 angles that have the same trigonometric values.
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Coterminal Angles
Angle Reduction to Least Positive Measure
Reducing an angle to its least positive coterminal measure involves finding the smallest positive angle between 0° and 360° that is coterminal with the given angle. This is done by repeatedly subtracting 360° until the angle lies within this range, ensuring the angle is positive and minimal.
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Modulo Operation in Angle Measurement
The modulo operation helps simplify angle measures by finding the remainder when the angle is divided by 360°. This remainder corresponds to the coterminal angle within one full rotation, making it a practical tool for quickly determining the least positive coterminal angle.
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