Question

An arc is subtended by a central angle measuring pi/2 radians. What fraction of the circumference is this arc?

Answer 1

Answer:

The angle is 1/4 the circumference is the arc

Step-by-step explanation:

To solve this, we are to set up a fractional relation between the central angle subtended by the arc and the total angle subtended by the circle.

At this point, we can note that the circumference of a circle actually subtends an angle of 2π radians at the center.

To express the angle subtended by the central angle [angle at the centre of the arc] as a fraction of the total circle, we do this:

The central angle of arc / total angle at the centre of the circle

= π/2 ÷2π

=$\pi/2 \times \frac{1}{2\pi}= 1/4$

Therefore the angle is 1/4 the circumference is the arc