What is the distance between the following polar coordinates?: $(5, \frac{- 5 π}{12}), (5, \frac{11 π}{6})$ $(5,(-5pi)/12), (5,(11pi)/6)$

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Answer 1 · 2017-06-18T08:38:37

$D = \sqrt{50 + 50 \frac{\sqrt{2}}{2}} \approx 9.2388$ $D=sqrt(50+50sqrt(2)/2)~~9.2388$

We are given

$r_{1} = 5$ $r_1=5$
$θ_{1} = - \frac{5 π}{12}$ $theta_1=-(5pi)/12$

$r_{2} = 5$ $r_2=5$
$θ_{2} = \frac{11 π}{6}$ $theta_2=(11pi)/6$

The distance formula for polar coordinates is

$D = \sqrt{r_{1}^{2} + r_{2}^{2} - 2 r_{1} r_{2} cos (θ_{1} - θ_{2})}$ $D=sqrt(r_1^2+r_2^2-2r_1 r_2 cos(theta_1 - theta_2))$

$D = \sqrt{5^{2} + 5^{2} - 2 (5) (5) cos (- \frac{5 π}{12} - \frac{11 π}{6})}$ $D=sqrt(5^2+5^2-2(5)(5)cos(-(5pi)/12-(11pi)/6))$

$D = \sqrt{25 + 25 - 50 cos (- \frac{9 π}{4})}$ $D=sqrt(25+25-50cos(-(9pi)/4))$

$D = \sqrt{50 + 50 \frac{\sqrt{2}}{2}} \approx 9.2388$ $D=sqrt(50+50sqrt(2)/2)~~9.2388$

What is the distance between the following polar coordinates?: (5,−5π12),(5,11π6) (5,(-5pi)/12), (5,(11pi)/6)