Textbook Question
Find the area of a sector of a circle having radius r and central angle θ. Express answers to the nearest tenth. See Example 5. r = 29.2 m, θ = 5π/6 radians
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 47
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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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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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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Related Practice
Textbook Question
Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).
139° 10'
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Textbook Question
Find a calculator approximation to four decimal places for each circular function value. cos (-0.2443)
Textbook Question
Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).
39°
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Textbook Question
Find a calculator approximation to four decimal places for each circular function value.
sin 1.0472
Textbook Question
Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).
174° 50'
5
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