What is the distance between $(2, \frac{5 π}{4})$ $(2 ,(5 pi)/4 )$ and $(8, \frac{11 π}{12})$ $(8 , (11 pi )/12 )$ ?

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What is the distance between $(2, \frac{5 π}{4})$ $(2 ,(5 pi)/4 )$ and $(8, \frac{11 π}{12})$ $(8 , (11 pi )/12 )$ ?

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Answer 1 · 2016-03-13T09:00:49

$7.211$ $7.211$

Explanation:

$(2, \frac{5 π}{4})$ $(2,(5pi)/4)$ in rectangular coordinates would be $(2 cos (\frac{5 π}{4}), 2 sin (\frac{5 π}{4}))$ $(2cos((5pi)/4), 2sin((5pi)/4))$ . As $sin (\frac{5 π}{4}) = - \frac{\sqrt{2}}{2}$ $sin((5pi)/4)=-sqrt2/2$ and $cos (\frac{5 π}{4}) = - \frac{\sqrt{2}}{2}$ $cos((5pi)/4)=-sqrt2/2$

This is $(- \sqrt{2}, - \sqrt{2})$ $(-sqrt2,-sqrt2)$ or $(- 1.4142, - 1.4142)$ $(-1.4142,-1.4142)$ .

$(8, \frac{11 π}{12})$ $(8,(11pi)/12)$ in rectangular coordinates would be $(8 cos (\frac{11 π}{12}), 8 sin (\frac{11 π}{12}))$ $(8cos((11pi)/12), 8sin((11pi)/12))$ . As $sin (\frac{11 π}{12}) = 0.2588$ $sin((11pi)/12)=0.2588$ and $cos (\frac{5 π}{4}) = - 0.9659$ $cos((5pi)/4)=-0.9659$

This is $(- 7.7272, 2.0704)$ $(-7.7272,2.0704)$ .

Hence distance between two is $\sqrt{({(- 7.7272 - (- 1.4142))}^{2} + ({(2.0704 - (- 1.4142))}^{2}}$ $sqrt{((-7.7272-(-1.4142))^2+((2.0704-(-1.4142))^2$

= $\sqrt{{(6.313)}^{2} + {(3.4846)}^{2}} = \sqrt{51.9964} = 7.211$ $sqrt{(6.313)^2+(3.4846)^2}=sqrt51.9964=7.211$

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What is the distance between $(2, \frac{5 π}{4})$ $(2 ,(5 pi)/4 )$ and $(8, \frac{11 π}{12})$ $(8 , (11 pi )/12 )$ ?

1 Answer

Explanation:

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What is the distance between $(2, \frac{5 π}{4})$ $(2 ,(5 pi)/4 )$ and $(8, \frac{11 π}{12})$ $(8 , (11 pi )/12 )$ ?