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.

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