What is the distance between the following polar coordinates?: # (10,(17pi)/12), (4,(15pi)/8) #

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Answer 1 · 2017-10-05T12:58:41

Distance between two points is #D= 10.27# unit

Polar coordinates of two points are #r_1=10 , theta_1=(17pi)/12 = #

#255^0 and r_2=4 , theta_2=(15pi)/8 = 337.5^0#

Cartesian coordinate of 1st point is # x_1= r_1cos theta_1#or

#x_1= 10 cos 255 ~~ -2.588 and y_1= r_1sin theta_1 = #

#y_1= 10 sin 255 ~~ -9.659 :. (-2.588,-9.659)#

Cartesian coordinate of 2nd point is # x_2= r_2cos theta_2#or

#x_2= 4 cos 337.5 ~~ 3.696 and y_2= r_2sin theta_2 = #

#y_2= 4 sin 337.5 ~~ -1.53 :. (3.696,-1.531)#

Distance between two points is

#D=sqrt( (x_1 − x_2)^2 + (y_1 − y_2)^2) =#

#D=sqrt( (-2.588 − 3.696)^2 + (-9.659 +1.531)^2) :. #

#D= 10.27# unit [Ans]