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Chapter 4: Problem 75

Is a degree or a radian the greater unit of measure? Explain.

Short Answer

Expert verified
In terms of units of measure, a degree is smaller than a radian. This is because 1 radian is equivalent to approximately 57.29 degrees.

Step by step solution

01

Understanding the Concept of a Degree

A degree is a unit of measurement for angles. The degree is typically denoted by the symbol 掳 and is equal to 1/360th of a complete circle. This is because a circle is divided into 360 equal parts, each of which is one degree.
02

Understanding the Concept of a Radian

A radian is another unit of measurement for angles. It is the standard unit of angular measure in most areas of mathematics. One radian is equal to the angle subtended at the center of a circle by an arc equal in length to the radius of the circle. This means that there are \(2\pi\) radians in a full circle, which is approximately equal to 6.28. Consequently, there are approximately 6.28 radians in a full circle, significantly less than the 360 degrees in a circle.
03

A Comparison between Degree and Radian

From the concepts explained in Step 1 and Step 2, it can be determined that there are 360 degrees and approximately 6.28 radians in a full circle. When comparing both units of measure, we can see that 1 degree equals approximately 0.01745 radians, and 1 radian equals approximately 57.29 degrees.

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