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Ch. 1 - Trigonometric Functions
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLial 12th EditionCh. 1 - Trigonometric FunctionsProblema 7
Capitolo 2, Problema 7

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. 119° 08' 03"

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1
To convert from degrees, minutes, and seconds (D° M' S") to decimal degrees, start by understanding the relationship: 1 degree = 60 minutes, and 1 minute = 60 seconds.
Convert the minutes to a decimal by dividing the number of minutes by 60: calculate \( \frac{8}{60} \).
Convert the seconds to a decimal by dividing the number of seconds by 3600 (since 1 degree = 3600 seconds): calculate \( \frac{3}{3600} \).
Add the degrees, the decimal minutes, and the decimal seconds together to get the decimal degrees: \( 119 + \frac{8}{60} + \frac{3}{3600} \).
To convert decimal degrees back to degrees, minutes, and seconds, separate the integer part as degrees, multiply the decimal part by 60 to get minutes, then multiply the decimal part of the minutes by 60 to get seconds, rounding seconds to the nearest whole number.

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Degrees, Minutes, and Seconds (DMS) Format

The DMS format expresses angles using three units: degrees (°), minutes ('), and seconds ("). One degree equals 60 minutes, and one minute equals 60 seconds. This system allows for precise representation of angles, commonly used in navigation and surveying.
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Conversion from Decimal Degrees to DMS

To convert decimal degrees to DMS, separate the integer part as degrees, multiply the fractional part by 60 to get minutes, then multiply the remaining fractional part by 60 again to get seconds. Rounding is often applied to the nearest second for practical accuracy.
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Conversion from DMS to Decimal Degrees

Converting DMS to decimal degrees involves adding degrees plus minutes divided by 60 plus seconds divided by 3600. This conversion simplifies calculations in trigonometry and other applications requiring decimal notation, with rounding typically to the nearest thousandth of a degree.
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