What is the distance between the following polar coordinates?: $(3,(7pi)/12), (1,(17pi)/8)$

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Answer 1 · 2017-06-07T10:50:06

$D~~3.04$

The distance formula for rectangular coordinates is

$D=sqrt((x_2-x_1)^2+(y_2-y_1)^2)$

Plugging in $x_n=r_ncos(theta_n)$ and $y_n=r_nsin(theta_n)$ , expanding, and simplifying gives

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

Plugging in $(r_1,theta_1)=(3,(7pi)/12)$ and $(r_2,theta_2)=(1,(17pi)/8)$

$D=sqrt(3^2+1^1-2(3)(1)cos((17pi)/8-(7pi)/12))$

$D=sqrt(10-6cos((37pi)/24))$

$D~~3.04$

What is the distance between the following polar coordinates?: (3,(7pi)/12), (1,(17pi)/8) (3,(7pi)/12), (1,(17pi)/8)