Textbook Question
Convert each angle measure to degrees, minutes, and seconds. If applicable, round to the nearest second. -25.485°
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Ch. 1 - Trigonometric Functions
Lial12th EditionTrigonometryISBN: 9780136552161
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Table of contents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Chapter 2, Problem 72
Convert each angle measure to degrees, minutes, and seconds. If applicable, round to the nearest second. 59.0854°
Verified step by step guidance1
Identify the given angle in decimal degrees: \(59.0854^\circ\).
Separate the whole number part from the decimal part. The whole number part is the degrees: \(59^\circ\).
Convert the decimal part (0.0854) to minutes by multiplying by 60: \(0.0854 \times 60\).
Separate the whole number part of the minutes from the decimal part. The whole number is the minutes.
Convert the remaining decimal part of the minutes to seconds by multiplying by 60, then round to the nearest second if necessary.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Decimal Degrees to Degrees, Minutes, and Seconds Conversion
This concept involves converting an angle expressed in decimal degrees into degrees, minutes, and seconds (D° M' S"). Degrees remain the integer part, minutes are obtained by multiplying the decimal remainder by 60, and seconds come from multiplying the remaining decimal after minutes by 60 again.
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Converting between Degrees & Radians
Rounding to the Nearest Second
After calculating seconds in the conversion process, it is often necessary to round the value to the nearest whole number to simplify the angle measure. This ensures the angle is expressed in a standard format suitable for practical use, such as navigation or surveying.
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4:45How to Use a Calculator for Trig Functions
Understanding Angle Measurement Units
Degrees, minutes, and seconds are units used to measure angles, where 1 degree equals 60 minutes and 1 minute equals 60 seconds. This hierarchical structure allows for precise representation of angles, especially when decimal degrees are not convenient or preferred.
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5:31Reference Angles on the Unit Circle
Related Practice
Textbook Question
Give all six trigonometric function values for each angle θ. Rationalize denominators when applicable. See Examples 5–7. tan θ = ―15/8 , and θ is in quadrant II .
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Textbook Question
Convert each angle measure to degrees, minutes, and seconds. If applicable, round to the nearest second. 102.3771°
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Textbook Question
Find the indicated function value. If it is undefined, say so. See Example 4. sin(―270°)
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Textbook Question
Find the indicated function value. If it is undefined, say so. See Example 4. tan 450°
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Textbook Question
Use identities to solve each of the following. Rationalize denominators when applicable. See Examples 5–7. Find cot θ , given that csc θ = ―1.45 and θ is in quadrant III.
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