Textbook Question
Convert each radian measure to degrees.
5π/4
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1. Measuring Angles
Complementary and Supplementary Angles
Problem 47
Textbook Question
Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).
42.5°
Verified step by step guidance1
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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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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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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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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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