Work against the angle of the force

A $45\ \text{N}$ pull moves a crate $12\ \text{m}$. You will make the program work out the work for every angle between the pull and the motion, from $0^\circ$ to $180^\circ$, and find where it halves and where it turns negative.

The idea. $W = Fd\cos\theta$: largest at $0^\circ$, zero at $90^\circ$, negative beyond.

Your tasks.

1. Work out the work at every angle in angles.
2. Find the angle at which the work is closest to half its largest value.
3. Find the smallest angle at which the work is negative.