What is the distance between #(2 , (5 pi)/8 )# and #(-1 , (1 pi )/3 )#?

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Answer 1 · 2016-10-22T19:45:59

The distance is #~~2.7#

Change the -1 radius to +1 by adding #pi# to the angle:

#(1, (4pi)/3)#

Find the difference between the two angles:

#theta = (4pi)/3 - (5pi)/8#

#theta = (32pi)/24 - (15pi)/24#

#theta = (17pi)/24#

We can find the distance between them using the Law of Cosines where side #a = 2#, side #b =1# and the angle between them is #theta = (17pi)/24#

#c^2 = 2^2 + 1^2 - 2(2)(1)cos((17pi)/24)#

#c ~~ 2.7#