What is the distance between the following polar coordinates?: $(1, \frac{π}{4}), (12, \frac{9 π}{8})$ $(1,(pi)/4), (12,(9pi)/8)$

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What is the distance between the following polar coordinates?: $(1, \frac{π}{4}), (12, \frac{9 π}{8})$ $(1,(pi)/4), (12,(9pi)/8)$

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Answer 1 · 2016-05-10T10:43:38

Distance $d = 12.92954402832$ $color(red)(d=12.92954402832" ")$ units

Explanation:

Distance between two polar coordinates formula

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

Solution:
Let $(r_{1}, θ_{1}) = (1, \frac{π}{4})$ $(r_1, theta_1)=(1, pi/4)$
Let $(r_{2}, θ_{2}) = (12, \frac{9 π}{8})$ $(r_2, theta_2)=(12, (9pi)/8)$

Use
$d = \sqrt{r_{1}^{2} + r_{2}^{2} - 2 \cdot r_{1} \cdot r_{2} \cdot cos (θ_{2} - θ_{1})}$ $d=sqrt(r_1^2+r_2^2-2*r_1*r_2*cos (theta_2-theta_1)$
$d = \sqrt{1^{2} + 12^{2} - 2 \cdot (1) \cdot (12) \cdot cos (\frac{9 π}{8} - \frac{π}{4})}$ $d=sqrt(1^2+12^2-2*(1)*(12)*cos ((9pi)/8-pi/4)$
$d = \sqrt{145 - 24 \cdot cos (\frac{7 π}{8})}$ $d=sqrt(145-24*cos ((7pi)/8))$
$d = 12.92954402832$ $color(red)(d=12.92954402832" ")$ units

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What is the distance between the following polar coordinates?: $(1, \frac{π}{4}), (12, \frac{9 π}{8})$ $(1,(pi)/4), (12,(9pi)/8)$

1 Answer

Explanation:

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What is the distance between the following polar coordinates?: (1,π4),(12,9π8) (1,(pi)/4), (12,(9pi)/8)

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What is the distance between the following polar coordinates?: $(1, \frac{π}{4}), (12, \frac{9 π}{8})$ $(1,(pi)/4), (12,(9pi)/8)$