What is the distance between the following polar coordinates?: # (2,(pi)/2), (2,(17pi)/12) #

1 Answer
Jan 1, 2018

#bar(AB)\approx3.9658#

Explanation:

Graph the two points:
Geogebra

A triangle is formed when the two points #A# and #B# are connected to the origin #O#. We know the angle #/_AOB# is #(17pi)/12-pi/2=(11pi)/12#, and the two sides #bar(AO)=bar(BO)=2#.

Then, #bar(AB)# can be found using the law of cosines:
#bar(AB)^2=bar(AO)^2+bar(BO)^2-2*bar(AO)*bar(BO)*cos(/_AOB)#
#bar(AB)^2=2^2+2^2-2*2*2*cos((11pi)/12)#
#bar(AB)^2\approx15.7274#

#thereforebar(AB)\approx3.9658#