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 = 12.7 cm, θ = 81°
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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 53
Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).
56° 25'
Verified step by step guidance1
Understand that to convert degrees and minutes to radians, you first need to convert the entire angle into decimal degrees. Recall that 1 minute (') is equal to \( \frac{1}{60} \) degrees.
Convert the given angle 56° 25' into decimal degrees using the formula: \( \text{Decimal degrees} = 56 + \frac{25}{60} \).
Use the conversion factor between degrees and radians: \( 1^{\circ} = \frac{\pi}{180} \) radians. Multiply the decimal degree value by \( \frac{\pi}{180} \) to convert to radians.
Write the expression for the angle in radians as \( \left(56 + \frac{25}{60}\right) \times \frac{\pi}{180} \).
If required, calculate the numerical value of the radians and round it 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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5:04
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 part. This step ensures the angle is expressed as a single decimal degree value before converting to radians.
Recommended video:
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. This is important for practical applications where exact values are not necessary.
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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 = 40.0 mi, θ = 135°
Textbook Question
Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).
122° 37'
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
Textbook Question
Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).
64.29°
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Textbook Question
Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).
85.04°
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