Textbook Question
In Exercises 29–34, convert each angle in degrees to radians. Round to two decimal places. -50°
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1. Measuring Angles
Radians
2:43 minutesProblem 40
Textbook Question
In Exercises 35–40, convert each angle in radians to degrees. Round to two decimal places.
-5.2 radians
Verified step by step guidance1
Recall the conversion formula from radians to degrees: \(\text{degrees} = \text{radians} \times \frac{180}{\pi}\).
Substitute the given radian measure into the formula: \(\text{degrees} = -5.2 \times \frac{180}{\pi}\).
Calculate the fraction \(\frac{180}{\pi}\) to get the approximate degree equivalent of one radian.
Multiply the radian value by the approximate degree equivalent to find the angle in degrees.
Round the resulting degree value to two decimal places as required.
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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
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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Converting between Degrees & Radians
Degree Measure
Degrees are another unit for measuring angles, where a full circle is divided into 360 equal parts. Degrees are often used in practical applications and are related to radians through a fixed conversion factor.
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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 fact that 2π radians equal 360 degrees. After conversion, rounding to the desired decimal places ensures precision.
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