Question

Points `(2 ,6 )` and `(5 ,3 )` are `(3 pi)/4` radians apart on a circle. What is the shortest arc length between the points?

Answer 1

I have taken you up to the final calculation point

Explanation:

`color(blue)("Determine the length AC")`

`AC=sqrt( (x_1-x_2)^2+(y_2-y_1)^2) = sqrt(18)=3sqrt(2)`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Determine the length AB")`

`/_ CAB = pi/2-(/_ABC)/2 = pi/2-(3pi)/8 = pi/8 ->(22 1/2 ^o)`

`ABcos(pi/8)= (3sqrt(2))/2`

`AB=(3sqrt(2))/(2cos(pi/8))`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("To determine arc length")`

This is radius times radian count

`ABxx (3pi)/4 =(3sqrt(2))/(2cos(pi/8)) xx(3pi)/4`

I will let you finish the calculation