What is the distance between the following polar coordinates?: (4,(-7pi)/12), (2,(pi)/8)

1 Answer
Jul 1, 2017

D~~5.4535

Explanation:

The distance formula for polar coordinates can be derived from the distance formula for rectangular coordinates

D=sqrt((x_2-x_1)^2+(y_2-y_1)^2)

Instead of using x and y values, though, we would just plug in their polar equivalents

x=rcos(theta)

y=rsin(theta)

Plugging those and using a couple of trigonometric identities, you get the following in purely polar coordinates

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

Plugging in the polar coordinates you have been given, we get

D=sqrt((4)^2+(2)^2-2(4)(2)cos(-(7pi)/12-pi/8))

D=sqrt(16+4-16cos(-(17pi)/24))

D~~sqrt(20-16(-0.60876))

D~~5.4535