Textbook Question
Find the angle of least positive measure that is coterminal with each angle. 792°
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1. Measuring Angles
Angles in Standard Position
2:55 minutesProblem 9
Textbook Question
Convert decimal degrees to degrees, minutes, seconds, and convert degrees, minutes, seconds to decimal degrees. If applicable, round to the nearest second or the nearest thousandth of a degree. 275.1005°
Verified step by step guidance1
To convert decimal degrees to degrees, minutes, and seconds (DMS), start by separating the whole number part from the decimal part. The whole number part is the degrees. For 275.1005°, the degrees are 275°.
Next, take the decimal part (0.1005) and multiply it by 60 to find the minutes: \(0.1005 \times 60\).
The whole number part of the result from step 2 is the minutes. Then, take the decimal part of that result and multiply it by 60 again to find the seconds.
Round the seconds to the nearest whole number to complete the DMS conversion.
To convert from degrees, minutes, and seconds back to decimal degrees, use the formula: \(\text{Decimal Degrees} = \text{Degrees} + \frac{\text{Minutes}}{60} + \frac{\text{Seconds}}{3600}\). Round the final decimal degrees to the nearest thousandth if required.
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Video duration:
2mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Decimal Degrees
Decimal degrees express angles as a single decimal number, combining degrees and fractional parts. For example, 275.1005° means 275 full degrees plus 0.1005 of a degree. This format is commonly used in calculations and digital applications for its simplicity.
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Degrees, Minutes, and Seconds (DMS) Format
DMS breaks down an angle into degrees, minutes, and seconds, where 1 degree = 60 minutes and 1 minute = 60 seconds. This format is traditional in navigation and surveying, providing a more precise and human-readable way to express angles.
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Conversion Between Decimal Degrees and DMS
Converting decimal degrees to DMS involves separating the integer degrees, multiplying the fractional part by 60 to get minutes, and then multiplying the remaining fraction by 60 to get seconds. The reverse process converts DMS back to decimal degrees by summing degrees plus minutes divided by 60 plus seconds divided by 3600.
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