What is the distance between polar coordinates #(2, 120^circ)# and #(1, 150^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 #(-4, -30^circ)# and #(3, 250^circ)#?
What is the distance between polar coordinates #(7, -150^circ)# and #(4, 130^circ)#?
What is the distance between polar coordinates #(-2, 300^circ)# and #(2, 10^circ)#?
What's the difference in finding the distance between two polar coordinates and two rectangular...

3797 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-09T06:28:33

#color(brown)("Distance " d = 1.2393#

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

#(r_1, theta_1) = (2, 120^@), (r_2, theta_2) = (1, 150^@)#

#d = sqrt(2^2 + 1^2 - 2 * 2 * 1 * cos (120-150)#

#d = sqrt (5 - 4 cos (-30)) ~~ 1.2393#