Question

What are the components of the vector between the origin and the polar coordinate `(9, (-pi)/4)`?

Answer 1

`x=(9sqrt2)/2`
`y=(-9sqrt2)/2`

Explanation:

Given `(r, theta)=(9, -pi/4)`

`x=r cos theta=9*cos (-pi/4)`
`x=9*1/sqrt2=9/sqrt2=(9*sqrt2)/(sqrt2)^2=(9sqrt2)/2`

`y=r sin theta=9*sin (-pi/4)`
`y=9*-1/sqrt2=-9/sqrt2=(-9*sqrt2)/(sqrt2)^2=(-9sqrt2)/2`

God bless....I hope the explanation is useful.