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 $theta = (17pi)/24$

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

$c ~~ 2.7$

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