Jaime makes the following claim.

Question

An angle with a measure of Latex: \frac{\pi}{3}
π
3
radians in a circle with a radius of Latex: 3
3
inches is smaller than an angle with a measure of Latex: \frac{\pi}{3}
π
3
radians in a circle with a radius of Latex: 6
6
inches. This is because the radian measure is based on the length of the radius of the circle and a radius of Latex: 3
3
inches is smaller than a radius of Latex: 6
6
inches.

Answer 1

The claim is incorrect. The measure of an angle in radians is not dependent on the length of the radius of the circle. Radians are a unit of angular measure that is defined based on the ratio of the arc length to the radius of the circle. Therefore, an angle with a measure of π/3 radians in a circle with a radius of 3 inches is equivalent to an angle with the same measure in a circle with a radius of 6 inches. The length of the radius does not affect the size or magnitude of the angle in radians.