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 49
Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).
139° 10'
Verified step by step guidance1
Understand that to convert degrees to radians, you use the formula: \(\text{radians} = \text{degrees} \times \frac{\pi}{180}\).
First, convert the given angle from degrees and minutes to decimal degrees. Since 1 minute is \(\frac{1}{60}\) of a degree, convert 10' to degrees by calculating \(10 \times \frac{1}{60}\).
Add this decimal value to the degrees part: \(139 + \frac{10}{60}\) to get the total degrees in decimal form.
Now, multiply the decimal degrees by \(\frac{\pi}{180}\) to convert the angle to radians: \(\left(139 + \frac{10}{60}\right) \times \frac{\pi}{180}\).
If required, use a calculator to approximate the value of \(\pi\) and perform the multiplication, then round the result 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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Converting between Degrees & Radians
Converting Minutes to Decimal Degrees
Angle measurements often include minutes (') where 1 degree equals 60 minutes. To convert minutes to decimal degrees, divide the minutes by 60 and add this to the degree value. This step ensures the angle is expressed as a decimal degree before converting to radians.
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5:04Converting between Degrees & Radians
Rounding to the Nearest Thousandth
After converting 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 in calculations or reporting.
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Related Practice
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
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°
2
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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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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 = 30.0 ft, θ = π/2 radians