What is the distance between $(1, \frac{3 π}{4})$ $(1 ,(3 pi)/4 )$ and $(3, \frac{15 π}{8})$ $(3 , (15 pi )/8 )$ ?

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What is the distance between $(1, \frac{3 π}{4})$ $(1 ,(3 pi)/4 )$ and $(3, \frac{15 π}{8})$ $(3 , (15 pi )/8 )$ ?

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Answer 1 · 2016-03-10T12:34:58

Distance between $(1, \frac{3 π}{4})$ $(1,(3pi)/4)$ and $(3, \frac{15 π}{8})$ $(3,(15pi)/8)$ is $3.9425$ $3.9425$

Explanation:

$(r, θ)$ $(r,theta)$ in polar coordinates is $(r cos θ, r sin θ)$ $(rcostheta,rsintheta)$ in rectangular coordinates.

Hence, $(1, \frac{3 π}{4})$ $(1,(3pi)/4)$ in rectangular coordinates is $(cos (\frac{3 π}{4}), sin (\frac{3 π}{4}))$ $(cos((3pi)/4),sin((3pi)/4))$ or $(- \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$ $(-sqrt2/2,sqrt2/2)$ or $(- 0.7071, 0.7071)$ $(-0.7071,0.7071)$

And $(3, \frac{15 π}{8})$ $(3,(15pi)/8)$ in rectangular coordinates is $(3 cos (\frac{15 π}{8}), 3 sin (\frac{15 π}{8}))$ $(3cos((15pi)/8),3sin((15pi)/8))$ or $(2.7716, - 1.1481)$ $(2.7716,-1.1481)$

Hence distance between $(- 0.7071, 0.7071)$ $(-0.7071,0.7071)$ and $(2.7716, - 1.1481)$ $(2.7716,-1.1481)$ is

$\sqrt{{(2.7716 + 0.7071)}^{2} + {(- 1.1481 - 0.7071)}^{2}}$ $sqrt((2.7716+0.7071)^2+(-1.1481-0.7071)^2)$ or
$\sqrt{{(3.4787)}^{2} + {(- 1.8552)}^{2}}$ $sqrt((3.4787)^2+(-1.8552)^2)$ or
$\sqrt{12.1014 + 3.4418} = \sqrt{15.5432} = 3.9425$ $sqrt(12.1014+3.4418)=sqrt(15.5432)=3.9425$

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What is the distance between $(1, \frac{3 π}{4})$ $(1 ,(3 pi)/4 )$ and $(3, \frac{15 π}{8})$ $(3 , (15 pi )/8 )$ ?

1 Answer

Explanation:

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What is the distance between (1,3π4)(1 ,(3 pi)/4 ) and (3,15π8)(3 , (15 pi )/8 )?

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What is the distance between $(1, \frac{3 π}{4})$ $(1 ,(3 pi)/4 )$ and $(3, \frac{15 π}{8})$ $(3 , (15 pi )/8 )$ ?