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

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Answer 1 · 2016-02-27T18:14:17

I have taken you up to the final calculation point

Tony B

#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