Question
Which equation is valid only when the angular measure is expressed in radians?
Answers
GPT 3.5
The equation that relates the arc length (s) of a circle to its radius (r) and central angle (θ) is valid only when the angular measure is expressed in radians.
The equation is:
s = rθ
This equation is derived from the definition of radian measure, where one radian is equal to the angle subtended by an arc length equal to the radius of the circle. Therefore, when using this equation, the value of the central angle (θ) must be in radians to be consistent with the arc length (s) and radius (r) units.
The equation is:
s = rθ
This equation is derived from the definition of radian measure, where one radian is equal to the angle subtended by an arc length equal to the radius of the circle. Therefore, when using this equation, the value of the central angle (θ) must be in radians to be consistent with the arc length (s) and radius (r) units.