What is the distance between the following polar coordinates?: # (6,(17pi)/12), (5,(9pi)/8) #

2 Answers
Apr 27, 2017
  1. They have different radii
  2. They have different angles

Explanation:

Polar coordinates are written in the following format:
#(r,\theta )#
Where #r# is the distance from the origin and #\theta# is the angle rotated counterclockwise about the origin from the x-axis. You can convert to polar coordinates by using the following formulas.
#x=rcos(\theta)#
#y=rsin(\theta)#
#tan(\theta)=\frac{y}{x}#
If you plot your points in either Cartesian or polar coordinates, you can clearly see the difference.

Apr 27, 2017

#"Distance "approx 10.42119#

Explanation:

#(6,frac{17pi}{12}),(5,frac{5pi}{8})#

Convert to Cartesian coordinates, remember the following formulas:
#color(red)(x=rcostheta)#
#color(red)(y=rsintheta)#

First coordinate: #(6,frac{17pi}{12})#
#x=6cos((17pi)/12)#

#y=6sin((17pi)/12)#

#color(blue)((6cos((17pi)/12),6sin((17pi)/12))#

Second coordinate: #(5,frac{5pi}{8})#
#x=5cos((5pi)/8)#

#y=5sin((5pi)/8)#

#color(blue)((5cos((5pi)/8),5sin((5pi)/8))#

Use the distance formula (Pythagorean Theorem) between these points:
#"Distance"=sqrt((6cos((17pi)/12)-5cos((5pi)/8))^2+(6sin((17pi)/12)-5sin((5pi)/8))^2)#

#"Distance "approx 10.42119#