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Chapter 4: Problem 125

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

Short Answer

Expert verified
A degree is a larger unit of measure compared to a radian.

Step by step solution

01

Understanding degrees

A full circle is divided into 360 degrees. This is a traditional way of representing angles and is widely used in various fields.
02

Understanding radians

A radian is defined as the angle subtended when the length of the arc is equal to the radius of the circle. This is a purer measurement in mathematics as it relates directly to circles. There are \(2\pi\) radians in a full circle, where \(\pi\) is approximately 3.14159.
03

Comparing Degrees and Radians

To compare these two units, it's important to note that \(2\pi\) radians is approximately \(6.28318\) which is equivalent to \(360^\circ\). Also, it's known that \(1^\circ\) equals to \(\frac{\pi}{180}\) radians, which is approximately \(0.01745\) radians. Therefore, a degree is larger than a radian.

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