Textbook Question
Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). 3600°
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1. Measuring Angles
Radians
Problem 33
Textbook Question
Convert each radian measure to degrees. See Examples 2(a) and 2(b). 11π/6
Verified step by step guidance1
Recall the conversion formula between radians and degrees: \(\text{Degrees} = \text{Radians} \times \frac{180}{\pi}\).
Identify the given radian measure: \(\frac{11\pi}{6}\).
Substitute the radian value into the conversion formula: \(\frac{11\pi}{6} \times \frac{180}{\pi}\).
Simplify the expression by canceling \(\pi\) in numerator and denominator: \(\frac{11}{6} \times 180\).
Multiply the fraction by 180 to find the degree measure: \(11 \times \frac{180}{6}\).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Radian Measure
A radian is a unit of angular measure based on the radius of a circle. One radian is the angle created when the arc length equals the radius. It is a standard unit in trigonometry, where 2π radians equal 360 degrees.
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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 can be further divided into minutes and seconds, but for most trigonometry problems, degrees are used as a straightforward measure of angle size.
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Conversion Between Radians and Degrees
To convert radians to degrees, multiply the radian measure by 180/π. This ratio comes from the equivalence of 2π radians to 360 degrees. For example, 11π/6 radians equals (11π/6) × (180/π) = 330 degrees.
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