Question

in the diagram below, \\( \theta \\) is measured in radians. which equation represents the relationship between the radius, \\( r \\), and arc length, \\( s \\)?
options:
\\( s = \theta \cdot r \\)
\\( r = \theta \cdot s \\)
\\( s = \theta + r \\)
\\( r = \theta + s \\)

Explanation:

Step1: Recall radian arc length formula

By definition, when an angle $\theta$ is in radians, the arc length $s$ subtended by the angle is proportional to the radius $r$ of the circle. The relationship is derived from the fact that 1 radian corresponds to an arc length equal to the radius.

Step2: Identify correct proportional relationship

The formula that relates arc length, radius, and central angle (in radians) is $s = \theta \cdot r$.

Answer:

$s = \Theta \cdot r$