# 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.
##(r,theta) -> (x,y)##
##(1,pi/4) -> (1/sqrt2,1/sqrt2)##
##(4,pi/2) -> (0,4)##
Choosing point 1 as ##(1/sqrt2,1/sqrt2)## and point 2 as ##(0,4)## 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##

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