Textbook Question
Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. ―203° 20'
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1. Measuring Angles
Angles in Standard Position
2:52 minutesProblem 95
Textbook Question
Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. -5280°
Verified step by step guidance1
Understand that coterminal angles differ by full rotations of 360°. To find an angle coterminal with the given angle, you add or subtract multiples of 360°.
Given the angle is \(-5280^\circ\), start by adding 360° repeatedly until you get an angle between 0° and 360°, which will be the least positive coterminal angle.
Express this mathematically as: \(\theta = -5280^\circ + 360^\circ \times k\), where \(k\) is an integer chosen so that \(0^\circ < \theta < 360^\circ\).
Calculate the value of \(k\) by dividing 5280 by 360 and finding the smallest integer \(k\) such that \(\theta\) is positive and less than 360°.
Once you find the correct \(k\), substitute back into the equation to find the least positive coterminal angle different from the original \(-5280^\circ\).
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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 adding or subtracting 360° until the angle lies within this range.
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Modulo Operation in Angle Measurement
Using modulo 360° arithmetic simplifies finding coterminal angles by effectively 'wrapping' the angle within a 0° to 360° cycle. The remainder after dividing the angle by 360° gives the equivalent angle within one full rotation, aiding in quick calculation of coterminal angles.
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