What is the distance the polar coordinates $(-2 ,( -3 )/8 )$ and $(4 ,(-7 pi )/4 )$ ?

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Answer 1 · 2018-02-21T10:29:04

Distance between the polar coordinates $color(brown)(d = 5.9066$

Using distance formula for polar coordinates,

$d = sqrt(r_1^2+r_2^2-2r_1r_2cos (theta_1 -theta_2))$

Given $r1 = -2, theta _1 = -(3/8), r_2 = 4, theta_2 = -((7pi)/4)$

Substituting the values in the formula,

$d = sqrt(-2^2 + 4^2 - (2 (-2) (4) cos (-(3/8) - ((-7pi)/4))$

$d = sqrt (4 + 16 +16 cos((14pi - 3)/8)$

$d = sqrt(20 + 16cos ((14pi - 3)/8) )= 5.9066$ units

What is the distance the polar coordinates (-2 ,( -3 )/8 )(-2 ,( -3 )/8 ) and (4 ,(-7 pi )/4 )(4 ,(-7 pi )/4 )?