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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 60
Capitolo 2, Problema 60

Convert each angle measure to decimal degrees. If applicable, round to the nearest thousandth of a degree. See Example 4(a). 38° 42' 18"

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1
Identify the components of the angle: degrees (°), minutes ('), and seconds ("). Here, the angle is 38° 42' 18".
Recall the conversion relationships: 1 minute (') = \(\frac{1}{60}\) degrees and 1 second (") = \(\frac{1}{3600}\) degrees.
Convert the minutes to decimal degrees by dividing the number of minutes by 60: \(42' = \frac{42}{60}\) degrees.
Convert the seconds to decimal degrees by dividing the number of seconds by 3600: \(18" = \frac{18}{3600}\) degrees.
Add the degrees, the converted minutes, and the converted seconds together to get the total angle in decimal degrees: \(38 + \frac{42}{60} + \frac{18}{3600}\). Then, round the result to the nearest thousandth of a degree if required.

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Degrees, Minutes, and Seconds (DMS) Notation

Angles can be expressed in degrees (°), minutes ('), and seconds ("), where 1 degree equals 60 minutes and 1 minute equals 60 seconds. This notation is commonly used in navigation and surveying to represent precise angle measurements.
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i & j Notation

Conversion from DMS to Decimal Degrees

To convert an angle from degrees, minutes, and seconds to decimal degrees, divide the minutes by 60 and the seconds by 3600, then add these values to the degrees. This process converts the angle into a single decimal number representing degrees.
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Converting Complex Numbers from Polar to Rectangular Form

Rounding Decimal Values

After conversion, decimal degrees are often rounded to a specified precision, such as the nearest thousandth. Rounding ensures the result is concise and practical for further calculations or applications.
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Sine, Cosine, & Tangent of 30°, 45°, & 60°
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