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

1 Answer
Jan 3, 2016

#5.8508# units

Explanation:

The distance formula for polar coordinates is

#d=sqrt(r_1^2+r_2^2-2r_1r_2Cos(theta_1-theta_2)#
Where #d# is the distance between the two points, #r_1#, and #theta_1# are the polar coordinates of one point and #r_2# and #theta_2# are the polar coordinates of another point.
Let #(r_1,theta_1)# represent #(4,(7pi)/4)# and #(r_2,theta_2)# represent #(3,(3pi)/8)#.
#implies d=sqrt(4^2+3^2-2*4*3Cos((7pi)/4-(3pi)/8)#
#implies d=sqrt(16+9-24Cos((11pi)/8)#
#implies d=sqrt(25-24*(-0.3847))=sqrt(25+9.2328)=sqrt(34.2328)=5.8508# units
#implies d=5.8508# units (approx)
Hence the distance between the given points is #5.8508#.