What is the distance between the following polar coordinates?: $(1, π), (4, π)$ $(1,pi), (4,pi)$

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Answer 1 · 2018-01-04T14:55:52

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:

$d = sqrt(1^2 + 4^2 - (2 xx 1 xx 4)cos(pi - pi))$

$d = sqrt(1 + 16 - 8cos(0))$

$d = sqrt(17 - (8 xx 1))$

$d = sqrt(17 - 8)$

$d = sqrt(9)$

$d = 3$

The distance between the two points is 3 units.

What is the distance between the following polar coordinates?: (1,pi), (4,pi) (1,π),(4,π) (1,pi), (4,pi)