Question

On the unit circle, if s is the length of the arc subtended by a central angle θ, measured in radians, then s = θ.

Answer 1

a. True The question is pretty much the entire definition of a radian. For an unit circle, its entire circumference is 2π and the entire circle has 2π radians. A quarter circle, or 90°, or π/2 radians, have 1/4th of the circumference. And 2π/4 is π/2. This natural relationship is WHY higher mathematics uses radians for the measurement of angles rather than arbitrary units such as degrees.