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Chapter 4: Problem 76

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

Short Answer

Expert verified
1 Radian is greater than 1 Degree. To be precise, 1 radian is approximately equal to 57.3 degrees.

Step by step solution

01

Understanding Degrees

A degree is a unit of measure for angles, which is represented by the symbol 掳. One degree is equivalent to \( \frac{1}{360} \)th of a full circle. That is to say, a full circle is 360 degrees.
02

Understanding Radians

A radian is another unit of measurement for angles, often used in mathematics. One radian is the angle made at the center of a circle by an arc whose length is equal to the radius of the circle. The full circle is about 6.28 radians (precisely \(2\pi\) radians).
03

Comparing Degrees and Radians

To understand which unit is bigger, we need to compare 1 degree with 1 radian. From understanding of Step 1 and 2, we know that a full cycle is 360 degrees and \(2\pi\) radians (approximately 6.28). Thus, 1 radian is approximately equal to \( \frac{360}{2\pi} \) or 57.3 degrees.

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