Find the distance between the points with polar coordinates (3, 120 degrees) and (0.5, 49
degrees)
Solution
The simplest way to solve this is to convert the polar coordinates into cartesian coordinates first,
and then, use the Cartesian coordinate distance formula to find the distance between those 2.
(Point 1 = P_1 = 3angle 120 implies (x,y) = (3 cos120^circ, 3sin120^circ) = (-
frac{3}{2}, frac{3sqrt{3}}{2}))
(Point 2 = P_2 = 0.5angle 49 implies (x,y) = (0.5 cos49^circ, 0.5sin49^circ) approx
(0.33, 0.38))
Now we use the distance formula:
(D = sqrt{(0.33-(-frac{3}{2}))^2 + (0.38-(frac{3sqrt{3}}{2})^2} approx 8.27) root
= 2.88