Question

For the given central angle, determine the distance traveled along the unit circle from the point (1, 0). 360 degrees a. 6.28 units clockwise c. 3.14 units clockwise b. 6.28 units d. 3.14 units

Answer 1

I can't give a "smart" explanation but the answer is D) 3.14 units

Answer 2

The length of a 180° arc of a unit circle is π ≈ 3.14 units.

Explanation:

Use your knowledge of the circumference of a circle (the length full around) and the fact that there are 360° in the central angle of a full circle. The distance around is proportional to the angle, so an arc of measure 180° will have a length equal to

... (180°/360°) × circumference = (1/2)×circumference

For a unit circle, the circumference is 2π (= π×diameter = 2π×radius). Half that length is π units.