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 52
Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).
85.04°
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: \(85.04^\circ \times \frac{\pi}{180}\).
Multiply the degree value by \(\pi\) to get \(85.04 \times \pi\) in the numerator.
Divide the result by 180 to complete the conversion to radians.
If needed, use a calculator to approximate the value and 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 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 is 2π times its radius. This relationship makes π a natural constant in angle measurement, linking linear and angular dimensions. Understanding this helps interpret radian values both symbolically and numerically.
Recommended video:
5:04Converting between Degrees & Radians
Rounding to the Nearest Thousandth
After 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. This is important for practical applications where exact values are unnecessary or unavailable.
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4:45How to Use a Calculator for Trig Functions
Related Practice
Textbook Question
Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).
122° 37'
Textbook Question
Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).
56° 25'
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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
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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