Question

What are the components of the vector between the origin and the polar coordinate `(5, (-11pi)/6)`?

Answer 1

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

`x=5cos(-(11pi)/6)=5(sqrt(3)/2)=(5sqrt(3))/2`
`y=5sin(-(11pi)/6)=5(1/2)=(5)/2`

So the rectangular form is `( (5sqrt(3))/2, (5)/2 )`.

Since we're talking about the component form of the vector, the initial point is `(0,0)`.

The component form of the vector is `[(5sqrt(3))/2, (5)/2 ]`.