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Ch. 3 - Radian Measure and The Unit Circle
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. 3 - Radian Measure and The Unit CircleProblema 44
Capitolo 4, Problema 44

Convert each radian measure to degrees. See Examples 2(a) and 2(b). 15π

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1
Recall the conversion formula between radians and degrees: \(\text{Degrees} = \text{Radians} \times \frac{180}{\pi}\).
Identify the given radian measure, which is \(15\pi\) radians.
Substitute \(15\pi\) into the conversion formula: \(15\pi \times \frac{180}{\pi}\).
Simplify the expression by canceling out \(\pi\) in the numerator and denominator.
Multiply the remaining numbers to find the equivalent degree measure.

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Radian Measure

A radian is a unit of angular measure based on the radius of a circle. One radian is the angle created when the arc length equals the radius. It is a standard unit in trigonometry and is related to degrees by the formula 180° = π radians.
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Converting between Degrees & Radians

Conversion Between Radians and Degrees

To convert radians to degrees, multiply the radian measure by 180/π. This conversion uses the equivalence that π radians equal 180 degrees, allowing angles expressed in radians to be expressed in degrees for easier interpretation.
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Converting between Degrees & Radians

Simplifying Expressions Involving π

When converting angles like 15π radians, it is important to treat π as a constant and simplify the expression by multiplying the numeric coefficient by 180. This helps in obtaining the degree measure without leaving π in the final answer.
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Simplifying Trig Expressions
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