What is the distance between the following polar coordinates?: # (2,(4pi)/3), (3,(7pi)/6) #

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Answer 1 · 2018-01-14T19:05:30

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(2^2 + 3^2 - (2 xx 2 xx 3)cos((4pi)/3 - (7pi)/6))#

#d = sqrt(4 + 9 - 12cos((2/2 xx (4pi)/3) - (7pi)/6))#

#d = sqrt(4 + 9 - 12cos((8pi)/6 - (7pi)/6))#

#d = sqrt(4 + 9 - 12cos((8pi - 7pi)/6))#

#d = sqrt(4 + 9 - 12cos(pi/6)#

#d = sqrt(13 - 10.392)#

#d = sqrt(2.608)#

#d = 1.615# rounded to the nearest thousandth.