What is the distance between polar coordinates #(-2, 300^circ)# and #(2, 10^circ)#?

Question

What is the formula for the distance between two polar coordinates?
How do I find the distance between polar coordinates #(2, 50^circ)# and #(5, -50^circ)#?
How do I find the distance between polar coordinates #(3, 60^circ)# and #(5, 145^circ)#?
How do I find the distance between the points with polar coordinates #(3, 120^circ)# and #(0.5,...
How do I find the distance between the points with polar coordinates #(2, 120^circ)# and #(1, 45^circ)#?
How do I find the distance between the points with polar coordinates #(2, 10^circ)# and #(7, 10^circ)#?
What is the distance between polar coordinates #(2, 120^circ)# and #(1, 150^circ)#?
What is the distance between polar coordinates #(-4, -30^circ)# and #(3, 250^circ)#?
What is the distance between polar coordinates #(7, -150^circ)# and #(4, 130^circ)#?
What's the difference in finding the distance between two polar coordinates and two rectangular...

4420 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-09T06:23:12

#color(indigo)("Distance " d ~~ 3.2766#

#d = sqrt (r_1^2 + r_2 ^2 - 2 r_1 r_2 cos (theta_1 - theta_2))#

#(r_1, theta_1) = (-2, 300^@), (r_2, theta_2) = (2, 10^@)#

#d = sqrt(-2^2 + 2^2 - 2 * -2 * 2 * cos (300-10)#

#d = sqrt (8 + 8 cos 290) ~~ 3.2766#