Question

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

Answer 1

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 = 7pi/6 - 12pi/6 + 8pi/6 = 3pi/6 = pi/2`

Because the angle between them is `pi/2`, we know that this is a 3,4,5 triangle.