- #1
gokuls
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I don't understand the intuition/proof of why arc length = arc angle * radius. This may be partially because I don't fully understand the concept of radians, but anyhow please help.
I don't understand the intuition/proof of why arc length = arc angle * radius. This may be partially because I don't fully understand the concept of radians, but anyhow please help.
I don't understand the intuition/proof of why arc length = arc angle * radius. This may be partially because I don't fully understand the concept of radians, but anyhow please help.
To help you (the OP, not LCKurtz) understand this a bit better, sketch a unit circle with its center at the origin. Draw a radius out from the center to the point (1, 0). Draw another radius from the center so that the radius makes an angle of 60° with the x-axis. Connect the two points where the two radii intersect the circle. You should have an equilateral triangle, with all three sides of length 1 and all three angles of measure 60°.You have the definition of a radian: 1 radian is measure of the central angle of a circle that subtends an arc of length equal to the radius of the circle.
Now say you have an arc of length ##s## subtended by a central angle ##\theta## measured in radians. Then, since the arc length is proportional to the central angle and a central angle of ##\theta= 1## radian subtends an arc of length ##r##,$$
\frac s \theta = \frac r 1$$which gives ##s = r\theta##.