What is the distance between $(2, \frac{5 π}{4})$ $(2 ,(5 pi)/4 )$ and $(- 2, \frac{11 π}{12})$ $(-2 , (11 pi )/12 )$ ?

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What is the distance between $(2, \frac{5 π}{4})$ $(2 ,(5 pi)/4 )$ and $(- 2, \frac{11 π}{12})$ $(-2 , (11 pi )/12 )$ ?

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Answer 1 · 2016-03-29T14:44:57

$s ≅ 3, 70 u n i t s$ $s~=3,70" "units$

Explanation:

$distance between two point for the polar form is given as:$ $"distance between two point for the polar form is given as:"$
$s = \sqrt{r_{1}^{2} + r_{2}^{2} - 2 \cdot r_{1} \cdot r_{2} \cdot cos (θ_{2} - θ_{1})}$ $s=sqrt(r_1^2+r_2^2-2*r_1*r_2*cos (theta_2-theta_1)$
$r_{1} = 2$ $r_1=2$
$r_{2} = - 2$ $r_2=-2$
$θ_{1} = \frac{5 π}{4}$ $theta_1=(5pi)/4$
$θ_{2} = \frac{11 π}{12}$ $theta_2=(11pi)/12$

$(θ_{2} - θ_{1}) = \frac{11 π}{2} - \frac{5 π}{4} = \frac{22 π - 5 π}{4} = \frac{17 π}{4}$ $(theta_2-theta_1)=(11pi)/2-(5pi)/4=(22pi-5pi)/4=(17pi)/4$

$s = \sqrt{2^{2} + {(- 2)}^{2} - 2 \cdot 2 \cdot (- 2) \cdot cos (\frac{17 π}{4})}$ $s=sqrt(2^2+(-2)^2-2*2*(-2)*cos ((17pi)/4)$

$s = \sqrt{4 + 4 + 8 \cdot cos (\frac{17 π}{4})}$ $s=sqrt(4+4+8*cos((17pi)/4)$

$s = \sqrt{8 + 8 \cdot 0, 707}$ $s=sqrt(8+8*0,707)$

$s = \sqrt{8 + 5, 656}$ $s=sqrt(8+5,656$
$s = \sqrt{13, 656}$ $s=sqrt(13,656)$

$s ≅ 3, 70 u n i t s$ $s~=3,70" "units$

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What is the distance between $(2, \frac{5 π}{4})$ $(2 ,(5 pi)/4 )$ and $(- 2, \frac{11 π}{12})$ $(-2 , (11 pi )/12 )$ ?

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Explanation:

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What is the distance between (2,5π4)(2 ,(5 pi)/4 ) and (−2,11π12)(-2 , (11 pi )/12 )?

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What is the distance between $(2, \frac{5 π}{4})$ $(2 ,(5 pi)/4 )$ and $(- 2, \frac{11 π}{12})$ $(-2 , (11 pi )/12 )$ ?