What is the distance between (1 ( pi)/4 ) and (4 ( pi )/2 )?

##~~3.37## I changed the points into Cartesian then used the Pythagoras distance equation
The distance ##S## between two points on a plane is given by:
##S = sqrt(Delta x^2 + Delta y^2)##
##S = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)##
And using a conversion formula:
##x = r cos theta##
##y = r sin theta##
It proves more convenient to change our points to Cartesian before using the distance equation.
##(rtheta) -> (xy)##
##(1pi/4) -> (1/sqrt21/sqrt2)##
##(4pi/2) -> (04)##
Choosing point 1 as ##(1/sqrt21/sqrt2)## and point 2 as ##(04)## we find:
##S = sqrt((0-1/sqrt2)^2 + (4-1/sqrt2)^2)##
##S = sqrt(1/2 + 16-8/sqrt2 +1/2)##
##S = sqrt(17-8/sqrt(2))##
At this point I gave up on getting a nice exact answer and used a calculator.
##S~~ 3.37##