Question

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

Answer 1

s = `sqrt` [25 + 16 - 2`xx` 5`xx` (- 4)`xx`cos(`pi/6` - `pi/4` )]
= `sqrt` [41+40cos`pi/12` ] = 8.999976 = 9 (nearly).

Explanation:

Let s be the distance between the points A(5, `pi/4` ) and B ( - 4, `pi/6` ). Then s = `sqrt` [`r_A^2` + `r_B^2` - 2`r_A` `r_B` cos(`theta_B` - `theta_A` )