What is the distance between the following polar coordinates?: # (1,pi), (4,pi) #

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Answer 1 · 2018-01-04T14:55:52

See a solution process below:

The formula for the distance between two polar coordinates is:

#d = sqrt(r_1^2 + r_2^2 - 2r_1r_2cos(Theta_1 - Theta_2))#

Where the two points are #(r_1, Theta_1)# and #(r_2, Theta_2)#

Substituting the values from the points in the problem gives:

#d = sqrt(1^2 + 4^2 - (2 xx 1 xx 4)cos(pi - pi))#

#d = sqrt(1 + 16 - 8cos(0))#

#d = sqrt(17 - (8 xx 1))#

#d = sqrt(17 - 8)#

#d = sqrt(9)#

#d = 3#

The distance between the two points is 3 units.