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Convert each radian measure to degrees. See Examples 2(a) and 2(b). 15π
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Ch. 3 - Radian Measure and The Unit Circle
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891
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TOC.tableOfContents
- 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
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Capitolo 4, Problema 47
Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).
42.5°
Guida verificata passo dopo passo1
Recall the formula to convert degrees to radians: \(\text{radians} = \text{degrees} \times \frac{\pi}{180}\).
Substitute the given degree measure into the formula: \(42.5^\circ \times \frac{\pi}{180}\).
Simplify the fraction by multiplying the numerator and denominator: \(\frac{42.5 \pi}{180}\).
Calculate the decimal value of the fraction \(\frac{42.5}{180}\) to get a decimal multiplier for \(\pi\).
Multiply the decimal by \(\pi\) (approximately 3.14159) and round the result to the nearest thousandth if required.
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Degree to Radian Conversion
Degrees and radians are two units for measuring angles. To convert degrees to radians, multiply the degree measure by π/180. This conversion is essential because radians are the standard unit in many mathematical contexts, especially calculus and trigonometry.
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Percorso guidato
5:04
Converting between Degrees & Radians
Use of π in Radian Measures
Radians are often expressed in terms of π because the circumference of a circle relates to π. For example, 180° equals π radians. Understanding this relationship helps in converting and simplifying angle measures in radians.
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Percorso guidato
5:04Converting between Degrees & Radians
Rounding to the Nearest Thousandth
After converting degrees to radians, the result may be an irrational number. Rounding to the nearest thousandth means keeping three decimal places, which balances precision and simplicity for practical use.
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Percorso guidato
4:45How to Use a Calculator for Trig Functions
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