Textbook Question
Convert each angle measure to degrees, minutes, and seconds. If applicable, round to the nearest second. -25.485°
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1. Measuring Angles
Angles in Standard Position
1:50 minutesProblem 79
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'
Verified step by step guidance1
Understand that coterminal angles differ by full rotations of 360°. To find angles coterminal with a given angle, you add or subtract multiples of 360°.
Convert the given angle 26° 30' into decimal degrees or work directly with degrees and minutes. Here, 30 minutes is half a degree, so 26° 30' = 26.5°.
To find the least positive coterminal angle different from 26° 30', subtract 360° from 26.5° to get a negative angle, which is not positive, so discard this.
Add 360° to 26.5° to find the next positive coterminal angle: 26.5° + 360° = 386.5°.
Convert the decimal coterminal angle back to degrees and minutes if needed. For example, 0.5° equals 30 minutes, so 386.5° = 386° 30'. This 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
Angle Measurement in Degrees and Minutes
Angles can be expressed in degrees (°) and minutes (') where 1 degree equals 60 minutes. Understanding how to convert and manipulate these units is essential for precise calculations, especially when adding or subtracting angles given in degrees and minutes.
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Least Positive Angle
The least positive angle coterminal with a given angle is the smallest positive angle greater than 0° that shares the same terminal side. It is found by adjusting the angle within the range of 0° to 360°, excluding the original angle, to find the minimal positive equivalent.
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