When determining radian measure, the units for the length of the intercepted arc and the radius have to be the same.Group of answer choicesTrueFalse
Question
When determining radian measure, the units for the length of the intercepted arc and the radius have to be the same.
- Group of answer choices
True
False
Solution
Answer
True
When determining the radian measure, the length of the intercepted arc and the radius must indeed have the same units. This is because the definition of a radian is based on the ratio of the length of the arc (s) to the radius (r) of the circle in which the arc is contained. The formula for the radian measure is given by:
where:
- is the angle in radians,
- is the length of the arc, and
- is the radius of the circle.
Since is a ratio, and must be expressed in the same units for the ratio to be dimensionally consistent.
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