Textbook Question
In Exercises 21β28, convert each angle in radians to degrees. -3π
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1. Measuring Angles
Radians
2:28 minutesProblem 37
Textbook Question
In Exercises 35β40, convert each angle in radians to degrees. Round to two decimal places. π/13 radians
Verified step by step guidance1
Recall the formula to convert radians to degrees: \(\text{degrees} = \text{radians} \times \frac{180}{\pi}\).
Substitute the given angle \(\frac{\pi}{13}\) radians into the formula: \(\text{degrees} = \frac{\pi}{13} \times \frac{180}{\pi}\).
Simplify the expression by canceling out \(\pi\): \(\text{degrees} = \frac{180}{13}\).
Divide 180 by 13 to get the decimal value of the angle in degrees.
Round the result 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 and is related to degrees by the formula 2Ο radians = 360 degrees.
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Converting between Degrees & Radians
Conversion Between Radians and Degrees
To convert radians to degrees, multiply the radian measure by 180/Ο. This conversion factor comes from the equivalence of 2Ο radians to 360 degrees, simplifying to 1 radian = 180/Ο degrees.
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Rounding Decimal Values
After converting the angle to degrees, round the result to the specified number of decimal places, in this case, two. Rounding ensures the answer is precise and presented in a standard format for clarity.
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