Textbook Question
Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement true.
sin s = 0.9918
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 62
Convert each radian measure to degrees. Write answers to the nearest minute. See Example 2(c).
9.84763
Verified step by step guidance1
Recall the conversion formula between radians and degrees: \(\text{degrees} = \text{radians} \times \dfrac{180}{\pi}\).
Multiply the given radian measure, 9.84763, by \(\dfrac{180}{\pi}\) to convert it to degrees: \(9.84763 \times \dfrac{180}{\pi}\).
Calculate the decimal degree value from the multiplication (do not round yet).
Separate the decimal degree value into its whole number part (degrees) and the fractional part (decimal minutes).
Convert the fractional part of the degrees to minutes by multiplying it by 60, then round the result to the nearest whole number to get the minutes.
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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 fractional minutes to the closest whole number. This ensures the angle measurement is precise and easy to communicate.
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Related Practice
Textbook Question
Convert each radian measure to degrees. Write answers to the nearest minute. See Example 2(c).
-5.01095
1
views
Textbook Question
Convert each radian measure to degrees. Write answers to the nearest minute. See Example 2(c).
0.3417
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