Points (3 ,2 ) and (8 ,4 ) are ( pi)/3 radians apart on a circle. What is the shortest arc length between the points?

1 Answer
Oct 3, 2016

s = (pisqrt29)/3

Explanation:

The square of distance, d, between the two points is:

d² = (8 - 3)² + (4 - 2)²

d² = (5)² + (2)²

d² = 29

d forms one side of a triangle where the other two sides are radii; this allow us the law of cosines to find the radius:

29 = r² + r² - 2(r)(r)cos(pi/3)#

r² = 29/(2 - 2cos(pi/3))

r = sqrt29

The arc length, s, is:

s = rtheta

s = (pisqrt29)/3