# What is the distance between the following polar coordinates?:  (3,(-4pi)/3), (4,(7pi)/6)

Oct 4, 2016

The origin (0, 0) and these two points form a 3,4,5 triangle. Therefore, the distance between the two points is 5.

#### Explanation:

Let's use the Law of Cosines to solve this problem:

c² = a² + b² - 2(a)(b)cos(C)

where $a = 3 , b = 4 ,$ and $C = 7 \frac{\pi}{6} - 12 \frac{\pi}{6} + 8 \frac{\pi}{6} = 3 \frac{\pi}{6} = \frac{\pi}{2}$

Because the angle between them is $\frac{\pi}{2}$, we know that this is a 3,4,5 triangle.