Question

What are the components of the vector between the origin and the polar coordinate `(12, (7pi)/8)`?

Answer 1

( `-`12 cos `pi`/8, 12 sin `pi`/8 ) =
( `-`6`sqrt`(2 + `sqrt`2 ). 6`sqrt`(2 `-` `sqrt`2 )
= ( `-`11.09, 4.59 ), nearly.

Explanation:

Components of radius vector to ( r, `theta` ) are ( r cos `theta`, r sin `theta` )
cos (`pi` - `theta` ) = `-` cos `theta`
sin (`pi` - `theta` ) = sin `theta`
cos `pi`/8 = `sqrt`((1 + cos `pi`/4)/2)
sin `pi`/8 = `sqrt`((1 `-` cos `pi`/4)/2)