What is the distance between #(5 ,(7 pi)/6 )# and #(3 , (- 7 pi )/8 )#?

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Answer 1 · 2017-08-13T12:48:45

The distance between two points is #2.06# unit.

First point conversion from polar coodinate to cartesian coordinate.

#r=5 , theta = (7*pi)/6=3.6652 # ,

x -cordinate is #r*cos theta =5 *cos(3.6652) ~~ -4.33#

y -cordinate is #r*sin theta =5 *sin(3.6652) ~~ -2.5#

Second point from polar coodinate to cartesian coordinate.

#r=3 , theta = 2pi- (-7*pi)/8=3.5343 # ,

x -cordinate is #r*cos theta =3 *cos(3.5343) ~~ -2.77#

y -cordinate is #r*sin theta =3 *sin(3.5343) ~~ -1.15#

Cartesian cordinates of two points are #(-4.33, -2.5) # and

# ( -2.77 , -1.15) . The distance between them is

#D= sqrt ((x_1-x_2)^2+ (y_1-y_2)^2) # or

#D= sqrt ((-4.33-(-2.77)^2+ (-2.5-(-1.15)^2) # or

#D ~~ 2.06# unit [Ans]