Textbook Question
Concept Check Classify each triangle as acute, right, or obtuse. Also classify each as equilateral, isosceles, or scalene. See the discussion following Example 2.
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1. Measuring Angles
Complementary and Supplementary Angles
Problem 42
Textbook Question
Convert each radian measure to degrees. See Examples 2(a) and 2(b). 11π/30
Verified step by step guidance1
Recall the conversion formula from radians to degrees: \(\text{degrees} = \text{radians} \times \frac{180}{\pi}\).
Identify the given radian measure: \(\frac{11\pi}{30}\).
Substitute the radian value into the conversion formula: \(\frac{11\pi}{30} \times \frac{180}{\pi}\).
Simplify the expression by canceling out \(\pi\) in numerator and denominator: \(\frac{11}{30} \times 180\).
Multiply the remaining numbers to find the degree measure: \(11 \times \frac{180}{30}\).
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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 and is related to degrees by the conversion factor 180°/π.
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Degree Measure
Degrees are a common unit for measuring angles, where a full circle is divided into 360 equal parts. Degrees are often used in practical applications and can be converted to and from radians using the relationship 180° = π radians.
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Conversion Between Radians and Degrees
To convert radians to degrees, multiply the radian value by 180/π. This conversion uses the equivalence of π radians to 180 degrees, allowing you to express angles in the more familiar degree measure.
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