Question

What is the distance between the following polar coordinates?: `(2,(pi)/4), (5,(5pi)/8)`

Answer 1

`4.6` to 2dp

Explanation:

If we denote `(2,pi/4)` by `A`, `(5,(5pi)/8)` by `B` and the origin by `O`, and the angle `angle AOB` by `theta`, Then:

`theta = (5pi)/8- pi/4 = (3pi)/8`

If we apply the cosine rule:

`a^2 = b^2 + c^2 - 2abcosA`

Then we get:

`(AB)^2 = (OA)^2 + (OB)^2 - 2(OA)(OB)costheta`
`" " = (2)^2 + (5)^2 - 2(2)(5)cos((3pi)/8)`
`" " = 4+25 - 20cos((3pi)/8)`
`" " = 29 - 20cos((3pi)/8)`
`" " = 21.34633...`

`:. AB = 4.629209`