Points #(2 ,5 )# and #(3 ,4 )# are #( pi)/3 # radians apart on a circle. What is the shortest arc length between the points?
2 Answers
The length of the arc is
Explanation:
The angle
The distance between the points is
This is the length of the chord
So,
The length of the arc is
Explanation:
Begin by finding the square of the length of the chord connecting the two points:
We can use a variant the Law of Cosines:
To find the radius of the circle, by letting,
We know that the arclength, s, between two points on a circle is the product of the radius and the radian measure of the central angle:
Substitute the values for