What is the distance between #(5 ,( pi)/4 )# and #(3 , (11 pi )/12 )#?

1 Answer
Burglar
May 25, 2016

The distance is #sqrt(19)#.

Explanation:

I asume that your two points are in polar coordinates.
If so, we have the two points:

#r_1=5, theta_1=pi/4#
#r_2=3, theta_2=11/12pi#

the distance of two points in polar coordinates is given by

#d=sqrt(r_1^2+r_2^2-2r_1r_2cos(theta_1-theta_2))#

for you this is

#d=sqrt(5^2+3^2-2*3*5*cos(pi/4-11/12pi))#
#d=sqrt(25+9-30cos(-2/3pi))#
#d=sqrt(34-30cos(2/3pi))#
#d=sqrt(34-30*1/2)#
#d=sqrt(19)#

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