Question7. Why do radian measurements not have a unit indicated? [2 marks]
Studdy Solution
STEP 1
1. Radian is a unit of angular measure.
2. The question is asking for an explanation of why radian measurements are typically written without a unit symbol.
STEP 2
1. Define what a radian is.
2. Explain the relationship between radians and other units.
3. Discuss why radians are dimensionless.
STEP 3
A radian is defined as the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle.
STEP 4
The relationship between radians and degrees is that radians is equal to degrees, or radians is equal to degrees.
STEP 5
Radians are considered dimensionless because they are defined as the ratio of two lengths (arc length divided by radius), which cancels out the units of length. Therefore, when expressing angles in radians, no unit is indicated because it is a pure number.
The reason radian measurements do not have a unit indicated is because they are dimensionless, being the ratio of arc length to radius, which cancels out the units of length.
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