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 44
Textbook Question
Convert each radian measure to degrees. See Examples 2(a) and 2(b). 15π
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, which is \(15\pi\) radians.
Substitute \(15\pi\) into the conversion formula: \(15\pi \times \frac{180}{\pi}\).
Simplify the expression by canceling out \(\pi\) in the numerator and denominator.
Multiply the remaining numbers to find the equivalent degree measure.
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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 formula 180° = π radians.
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Converting between Degrees & Radians
Conversion Between Radians and Degrees
To convert radians to degrees, multiply the radian measure by 180/π. This conversion uses the equivalence that π radians equal 180 degrees, allowing angles expressed in radians to be expressed in degrees for easier interpretation.
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Simplifying Expressions Involving π
When converting angles like 15π radians, it is important to treat π as a constant and simplify the expression by multiplying the numeric coefficient by 180. This helps in obtaining the degree measure without leaving π in the final answer.
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