Question

What are the components of the vector between the origin and the polar coordinate `(5, (pi)/8)`?

Answer 1

`(4.619, 1.913)`

Explanation:

First off, acknowledge the fact that the question is simply asking you to convert from the polar coordinate to rectangular, namely, x and y components. From here, we will be using a few givens:
`(1)` Polar coordinates take the form `(r, theta)`
`(2)` `x = rcos(theta)`
`(3)` `y = rsin(theta)`

Now we simply evaluate `(2)` and `(3)` using `r = 5` and `theta = pi/8`.

Thus, our components are `(4.619, 1.913)`, and we are done.