What is the distance between the following polar coordinates?: # (3,(17pi)/12), (-8,(5pi)/8) #

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Answer 1 · 2018-01-15T12:46:07

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(3^2 + (-8)^2 - (2 * 3 * -8)cos((17pi)/12 - (5pi)/8))#

#d = sqrt(9 + 64 - (-48)cos((2/2 xx (17pi)/12) - (3/3 xx (5pi)/8))#

#d = sqrt(73 + 48cos((34pi)/24 - (15pi)/24))#

#d = sqrt(73 + 48cos((34pi - 15pi)/24))#

#d = sqrt(73 + 48cos((19pi)/24))#

#d = sqrt(73 + (48 * -0.793))#

#d = sqrt(73 + (-38.081))#

#d = sqrt(34.919)#

#d = 5.909# rounded to the nearest thousandth.