What is the distance between the following polar coordinates?: # (7,(23pi)/12), (9,(11pi)/8) #

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Answer 1 · 2018-02-20T19:34:48

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(7^2 + 9^2 - (2 xx 7 xx 9 xx cos((23pi)/12 - (11pi)/8)))#

#d = sqrt(49 + 81 - (126 xx cos((46pi)/24 - (33pi)/24)))#

#d ~= sqrt(130 - (126 xx -0.13))#

#d ~= sqrt(130 - (-16.38))#

#d ~= sqrt(130 + 16.38)#

#d ~= sqrt(146.38)#

#d ~= 12.10#