# What is the distance between the following polar coordinates?:  (9,(17pi)/12), (4,(3pi)/8)

Mar 25, 2017

Using the Law of Cosines

#### Explanation:

Plotting these two points, there is a triangle formed whose central angle measures
$3 \frac{\pi}{8} + 7 \frac{\pi}{12} = 23 \frac{\pi}{24}$
By the Law of Cosines, the distance, c, between the points is found by
${c}^{2} = {9}^{2} + {4}^{2} - \left(9\right) \left(4\right) \cos \left(\frac{23 \pi}{24}\right)$
That is...
${c}^{2} = 97 - 36 \cos \left(\frac{23 \pi}{24}\right)$
The value of c is the positive square root of the expression on the right side.