Question

What is the distance between `(4 ,( 9 pi)/8 )` and `(-4 ,( 3pi )/2 )`?

Answer 1

`6.6517\ \text{unit}`

Explanation:

The distance between the points `(r_1, \theta_1)\equiv(4, {9\pi}/8)` & `(r_2, \theta_2)\equiv(-4, {3\pi}/2)` is given by the formula as follows

`\sqrt{r_1^2+r_2^2-2r_1r_2\cos(\theta_1-\theta_2)}`

`=\sqrt{4^2+(-4)^2-2(4)(-4)\cos({9\pi}/8-{3\pi}/2)}`

`=\sqrt{32+32\cos({3\pi}/8)}`

`=4\sqrt2\sqrt{1+\sin({\pi}/8)}`

`=6.6517\ \text{unit}`