Textbook Question
In Exercises 2β4, convert each angle in degrees to radians. Express your answer as a multiple of π. 15Β°
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1. Measuring Angles
Radians
2:00 minutesProblem 7
Textbook Question
In Exercises 5β7, convert each angle in radians to degrees. - 5π 6
Verified step by step guidance1
Recall the conversion formula from radians to degrees: \(\text{Degrees} = \text{Radians} \times \dfrac{180}{\pi}\).
Identify the given angle in radians: \(\dfrac{5\pi}{6}\).
Substitute the given angle into the conversion formula: \(\dfrac{5\pi}{6} \times \dfrac{180}{\pi}\).
Simplify the expression by canceling \(\pi\) in numerator and denominator: \(\dfrac{5}{6} \times 180\).
Multiply the remaining numbers to find the angle in degrees: \(5 \times \dfrac{180}{6}\).
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Video duration:
2mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Radian Measure
Radian is a unit of angular measure based on the radius of a circle. One radian is the angle subtended at the center of a circle by an arc equal in length to the radius. It provides a natural way to measure angles in terms of the circle's geometry.
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Degree Measure
Degrees are a common unit for measuring angles, where a full circle is divided into 360 equal parts. Each degree represents 1/360 of a full rotation, making it intuitive for everyday use and practical applications.
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Conversion between Radians and Degrees
To convert radians to degrees, multiply the radian value by 180/Ο. This conversion factor arises because Ο radians equal 180 degrees. For example, converting 5Ο/6 radians involves multiplying by 180/Ο to find the equivalent degree measure.
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