Textbook Question
Convert each radian measure to degrees. Write answers to the nearest minute. See Example 2(c).
3.06
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 61
Convert each radian measure to degrees. Write answers to the nearest minute. See Example 2(c).
0.3417
Verified step by step guidance1
Recall the conversion formula between radians and degrees: \(\text{Degrees} = \text{Radians} \times \dfrac{180}{\pi}\).
Substitute the given radian measure into the formula: \(\text{Degrees} = 0.3417 \times \dfrac{180}{\pi}\).
Calculate the decimal degree value from the multiplication (do not round yet).
Separate the decimal degree into whole degrees and the fractional part. The whole number part is the degrees.
Convert the fractional part of the degree into minutes by multiplying it by 60, then round to the nearest whole minute.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Radian to Degree Conversion
Radians and degrees are two units for measuring angles. To convert radians to degrees, multiply the radian measure by 180/π. This conversion is essential because degrees are often easier to interpret in practical contexts.
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Converting between Degrees & Radians
Degrees, Minutes, and Seconds
Degrees can be subdivided into minutes and seconds, where 1 degree equals 60 minutes and 1 minute equals 60 seconds. Writing answers to the nearest minute means converting the decimal part of degrees into minutes by multiplying by 60.
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5:04Converting between Degrees & Radians
Rounding to the Nearest Minute
After converting the decimal degrees to minutes, rounding to the nearest minute involves approximating the value to the closest whole number. This ensures the answer is precise and presented in a standard angular format.
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Related Practice
Textbook Question
Convert each radian measure to degrees. Write answers to the nearest minute. See Example 2(c).
9.84763
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Textbook Question
Work each problem. See Example 5. Irrigation Area A center-pivot irrigation system provides water to a sector-shaped field as shown in the figure. Find the area of the field if θ = 40.0° and r = 152 yd.
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Textbook Question
Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement true.
tan s = 0.2126
Textbook Question
Work each problem. See Example 5. Arc Length A circular sector has an area of 50 in² . The radius of the circle is 5 in. What is the arc length of the sector?
Textbook Question
Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement true.
cos s = 0.7826