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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 8
Capitolo 2, Problema 8

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. 47° 25' 11"

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To convert from degrees, minutes, and seconds (D° M' S") to decimal degrees, use the formula: \(\text{Decimal Degrees} = D + \frac{M}{60} + \frac{S}{3600}\).
Identify the values from the given angle: \(D = 47\), \(M = 25\), and \(S = 11\).
Substitute these values into the formula: \(47 + \frac{25}{60} + \frac{11}{3600}\).
Calculate each fractional part separately: \(\frac{25}{60}\) converts minutes to degrees, and \(\frac{11}{3600}\) converts seconds to degrees.
Add all parts together to get the decimal degree value, then round to the nearest thousandth if required.

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Degrees, Minutes, and Seconds (DMS) Format

Degrees, minutes, and seconds is a way to express angles where one degree is divided into 60 minutes, and one minute into 60 seconds. This format is commonly used in navigation and geography to provide precise angular measurements.
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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 accuracy.
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Conversion from DMS to Decimal Degrees

To convert DMS to decimal degrees, divide the minutes by 60 and the seconds by 3600, then add these values to the degrees. This conversion simplifies calculations and is useful in many trigonometric and geographic applications.
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