Question

What are the components of the vector between the origin and the polar coordinate `(-1, (3pi)/4)`?

Answer 1

`[ sqrt(2)/2, -sqrt(2)/2 ]`

Explanation:

We can use `x=rcos(theta)` and `y=rsin(theta)` to convert:

`x=-1cos((3pi)/4)=-1(-sqrt(2)/2)=sqrt(2)/2`
`y=-1sin((3pi)/4)=-1(sqrt(2)/2)=-sqrt(2)/2`

So the vector is `[ sqrt(2)/2, -sqrt(2)/2 ]`.