What is the distance between $(3, \frac{5 π}{6})$ $(3 ,(5 pi)/6 )$ and $(- 2, \frac{5 π}{12})$ $(-2 , (5 pi )/12 )$ ?

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Answer 1 · 2017-11-09T17:08:20

$208.028$ $208.028$

( 3 .d.p. )

First you need to convert the polar coordinates into Cartesian coordinates. This can be done using the following:

$x = r cos (θ)$ $x= rcos(theta)$

$y = r sin (θ)$ $y= rsin(theta)$

$:.$

$x= 3cos((5pi)/6)=-2.598$ ( 3 .d.p.)

$y=3sin((5pi)/6)=1.500$

$color(blue)((-2.598 , 1.500)$

$x=-2cos((5pi)/12)=-0.518$

$=-2sin((5pi)/12)=-1.932$

$color(blue)(( -0.518 , -1.932 )$

Using the distance formula:

$d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2$

$d= sqrt((-2.598-(-0.518))^2+(1.500-(-1.932))^2$

$d= sqrt((-208)^2+(3.432)^2)=208.0283121=208.028$

( 3 .d.p. )

What is the distance between (3 ,(5 pi)/6 )(3,5π6)(3 ,(5 pi)/6 ) and (-2 , (5 pi )/12 )(−2,5π12)(-2 , (5 pi )/12 )?