Question

Points `(8 ,5 )` and `(3 ,4 )` are `( pi)/3` radians apart on a circle. What is the shortest arc length between the points?

Answer 1

Let me give you a starting point:

Explanation:

Distance between `P_1" and "P_2` is

`sqrt((8-5)^2+(5-4)^2)" "=" "sqrt(26)`

Then use `" "rsin(pi/6)" "=" "P_1P_3" "=" "sqrt(26)/2`

So `" "r = sqrt(26)/(2sin(pi/6))`

From which you can derive the length of arc