What is the distance between the following polar coordinates?: # (3,(23pi)/12), (7,(13pi)/8) #

1 Answer
Apr 13, 2016

The distance between the two points is #5.7#

Explanation:

It's easier to calculate with cartesian coordinates than with polar, so my advice is to start with converting #(3;(23pi)/12)# and #(7;(13pi)/8)# to #(x_1;y_1)# and #(x_2;y_2)#

The relationship between #color(blue)(cartesian)# and #color(red)(polar)# coordinates is:

#color(blue)(x)=color(red)(R cdot cos(theta)#
#color(blue)(y)=color(red)(R cdot sin(theta)#

For your first point:
#R=3#
#theta=(23pi)/12#

For your second point:
#R=7#
#theta=(13pi)/8#

The distance between two points is:
#d=sqrt((x_1-x_2)^2+(y_1-y_2)^2)#

#=sqrt((3cos((23pi)/12)-7cos((13pi)/8))^2+(3sin((23pi)/12)-7sin((13pi)/8))^2)#

#=sqrt((3cos(-pi/12)-7cos(-(3pi)/8))^2+(3sin(-pi/12)-7sin(-(3pi)/8))^2)#

#=sqrt((3cos(pi/12)-7cos((3pi)/8))^2+(7sin((3pi)/8)-3sin(pi/12))^2)#

#~~5.7#