Textbook Question
Convert each angle measure to degrees, minutes, and seconds. If applicable, round to the nearest second. 122.6853°
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1. Measuring Angles
Angles in Standard Position
2:11 minutesProblem 92
Textbook Question
Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. 1000°
Verified step by step guidance1
Understand that angles are coterminal if they differ by a full rotation of 360°. This means we can add or subtract multiples of 360° to find coterminal angles.
Since the given angle is 1000°, to find a coterminal angle with the least positive measure (other than 1000° itself), subtract multiples of 360° until the result is between 0° and 360°.
Set up the expression: \(1000° - 360° \times n\), where \(n\) is an integer chosen so that the result lies in the interval \((0°, 360°)\).
Calculate the appropriate value of \(n\) by dividing 1000 by 360 and taking the integer part: \(n = \lfloor \frac{1000}{360} \rfloor\).
Subtract \(360° \times n\) from 1000° to find the coterminal angle with the least positive measure different from 1000°.
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Video duration:
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 represent the same direction in standard position.
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Coterminal Angles
Angle Measurement and Positive Angles
Angles can be measured in degrees, and positive angles are measured counterclockwise from the positive x-axis. The least positive coterminal angle is the smallest positive angle greater than 0° that is coterminal with the given angle, ensuring it is not equal to the original angle.
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Modulo Operation in Angle Reduction
Finding the least positive coterminal angle involves using the modulo operation with 360°, which effectively reduces any angle to its equivalent between 0° and 360°. This operation simplifies large angles by removing full rotations, making it easier to identify the smallest positive coterminal angle.
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