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