Textbook Question
Convert each angle measure to degrees, minutes, and seconds. If applicable, round to the nearest second. 59.0854°
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1. Measuring Angles
Angles in Standard Position
1:22 minutesProblem 84
Textbook Question
Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. ―203° 20'
Verified step by step guidance1
First, 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°.
Convert the given angle from degrees and minutes to a decimal degree format for easier calculation. Recall that 1 minute = 1/60 degrees, so convert 20' to degrees by calculating \(20 \div 60\).
Express the given angle as a decimal: \(-203° - \frac{20}{60}° = -203.3333°\) (approximately).
To find the least positive coterminal angle, add 360° to the given angle: \(-203.3333° + 360°\).
If the result is still negative or zero, continue adding 360° until the angle is positive and less than 360°. This final positive angle is the least positive coterminal angle different from the original.
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Video duration:
1mKey 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 position on the unit circle.
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Coterminal Angles
Converting Between Degrees and Minutes
Angles expressed in degrees and minutes require understanding that 1 degree equals 60 minutes. When performing arithmetic operations, convert minutes to decimal degrees or handle minutes separately to maintain accuracy. This is essential for precise calculations involving angles given in degrees and minutes.
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Finding the Least Positive Coterminal Angle
The least positive coterminal angle is the smallest positive angle greater than 0° that is coterminal with the given angle. To find it, add 360° repeatedly until the angle is positive and less than 360°, ensuring it is not equal to the original angle. This process locates the equivalent angle within the standard 0° to 360° range.
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