What is the distance between the following polar coordinates?: # (3,(3pi)/4), (2,(7pi)/8) #

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Answer 1 · 2017-07-04T22:03:58

#1.383# #"units"#

We can do this by converting each coordinate to the equivalent Cartesian (rectangular) form, and using the distance formula:

#x = rcostheta#

#y = rsintheta#

#x_1 = 3cos((3pi)/4) = -2.121#

#y_1 = 3sin((3pi)/4) = 2.121#

#x_2 = 2cos((7pi)/8) = -1.848#

#y_2 = 2sin((7pi)/8) = 0.765#

#"distance" = sqrt((-2.121 - (-1.848))^2 + (2.121 - 0.765)^2)#

#= color(blue)(1.383# #color(blue)("units"#