Question

What are the components of the vector between the origin and the polar coordinate `(-16, (-pi)/4)`?

Answer 1

`x = -16 * cos (-pi/4 )= -16 * (1/sqrt2) = color (green)(-8sqrt2`

`y = -16 * sin (-pi/4 )= -16 * (-1/sqrt2) = color (green)(8sqrt2`

Explanation:

We can use the following formulas to convert polar to Cartesian coordinates.

`x = r cos theta, y = r sin theta`

`Given : [r,theta] = [-16, -pi/4]`

`x = -16 * cos (-pi/4 )= -16 * (1/sqrt2) = color (green)(-8sqrt2`

`y = -16 * sin (-pi/4 )= -16 * (-1/sqrt2) = color (green)(8sqrt2`

`tan theta = tan (-pi/4) = -1`