What is the distance between the following polar coordinates?: # (2,(12pi)/8), (7,(7pi)/8) #

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Answer 1 · 2018-01-07T13:14:46

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

#d = sqrt(4 + 49 - (28cos((12/8 - 7/8)pi)))#

#d = sqrt(53 - (28 xx -0.383))# Rounded to the nearest Thousandth.

#d = sqrt(53 - (-10.724))#

#d = sqrt(53 + 10.724)#

#d = sqrt(63.724)#

#d = 7.983# Rounded to the Nearest Thousandth.

Or the distance is approximately 8 units.