Answer
The distance between the two points is $~~2\sqrt{7}$
Work Step by Step
We can find the Cartesian coordinates of the first point:
$x_1 = 4~cos~\frac{4\pi}{3} = -2$
$y_1 = 4~sin~\frac{4\pi}{3} = -3.464$
We can find the Cartesian coordinates of the second point:
$x_2 = 6~cos~\frac{5\pi}{3} = 3$
$y_2 = 6~sin~\frac{5\pi}{3} = -5.196$
We can find the distance between the two points:
$d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
$d = \sqrt{(3-(-2))^2+(-5.196-(-3.464))^2}$
$d = \sqrt{28}$
$d = 2\sqrt{7}$
The distance between the two points is $~~2\sqrt{7}$
