Textbook Question
Convert each radian measure to degrees.
5π/4
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1. Measuring Angles
Complementary and Supplementary Angles
Problem 45
Textbook Question
Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).
39°
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: \(39^\circ \times \frac{\pi}{180}\).
Simplify the fraction \(\frac{39}{180}\) by dividing numerator and denominator by their greatest common divisor.
Express the result as a multiple of \(\pi\), for example, \(\frac{39}{180} \pi\) or its simplified form.
If a decimal approximation is needed, multiply the simplified fraction by the approximate value of \(\pi \approx 3.1416\) and round to the nearest thousandth.
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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 trigonometric calculations.
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Use of π in Radian Measures
Radians are often expressed in terms of π to maintain exact values. For example, 180° equals π radians. Understanding how to represent angles using π helps in simplifying trigonometric expressions and solving problems accurately.
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Rounding to the Nearest Thousandth
When converting degrees to radians, the result may be an irrational number. Rounding to the nearest thousandth means limiting the decimal places to three digits, which balances precision and simplicity for practical use.
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