Textbook Question
Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).
42.5°
1
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Ch. 3 - Radian Measure and The Unit Circle
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 4, Problem 45
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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Related Practice
Textbook Question
Convert each radian measure to degrees. See Examples 2(a) and 2(b). 15π
1
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Textbook Question
Find a calculator approximation to four decimal places for each circular function value. See Example 3.
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Textbook Question
Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).
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2
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Textbook Question
Find a calculator approximation to four decimal places for each circular function value. cos (-0.2443)
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Find a calculator approximation to four decimal places for each circular function value.
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