What is the distance between the following polar coordinates?: # (3,(15pi)/8), (9,(-2pi)/8) #

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Answer 1 · 2017-11-20T12:48:17

Distance is #6.33 #unit

Polar coordinates of point A is #r_1=3.0 , theta_1=(15pi)/8=337.5^0#

Polar coordinates of point B is #r_2=9, theta_2=-(2pi)/8 , theta_2=-45^0=315^0#

Cartesian coordinates of point A is #x_1=r_1 cos theta_1 #

or # x_1= 3.0 cos 337.5 ~~ 2.77, y_1=r_1 sin theta # or

#y_1=3.0 sin 337.5 ~~-1.15 :. # Cartesian coordinates of

point A is #(x_1,y_1) or (2.77, -1.15)#

Cartesian coordinates of point B is #x_2=r_2 cos theta_2 #

or # x_2= 9.0 cos 315 = 6.36, y_2=r_2 sin theta_2 # or

#y_2=9.0 sin 315=-6.36 #. Cartesian coordinates of

point B is #(x_2,y_2) or (6.36,-6.36)#

Distance between them #D= sqrt ((x_1-x_2)^2+(y_1-y_2)^2#

#D= sqrt ((2.77-6.36)^2+(-1.15+6.36)^2) ~~ 6.33#unit [Ans]