# What is the distance between (5 ,( pi)/4 ) and (-4 , ( pi )/6 )?

s = sqrt [25 + 16 - 2$\times$ 5$\times$ (- 4)$\times$cos($\frac{\pi}{6}$ - $\frac{\pi}{4}$ )]
= sqrt [41+40cos$\frac{\pi}{12}$ ] = 8.999976 = 9 (nearly).
Let s be the distance between the points A(5, $\frac{\pi}{4}$ ) and B ( - 4, $\frac{\pi}{6}$ ). Then s = sqrt [${r}_{A}^{2}$ + ${r}_{B}^{2}$ - 2${r}_{A}$ ${r}_{B}$ cos(${\theta}_{B}$ - ${\theta}_{A}$ )