Find the measure of a central angle 𝜃 in a circle of radius 1 if 𝜃 subtends an arc of length 𝜋/6. Give 𝜃 in radians and degrees.

Answer 1

Angle theta = pi/6 = 30 degrees

angle times radius = arc length if the angle is measured in radians

1 x pi/6 = pi/6

for example if the central angle were 360 degrees = 2pi and radius = 1, then the circumference = 2pi(1) = 1

that's the formula for the circumference of a circle: pi x diameter = pi (2r) = pi(2x1) = 2pi