Sine & cosine values
It is not easy to figure out the actual values of cosine and sine to different angles. Only a few angles are obvious:
- an angle of $0^\circ$ of course has no vertical part, so $\sin(0^\circ)=0$, and its horizontal part moves the full 1 unit, so $\cos(0^\circ)=1$.
- We have the same in the opposite $180^\circ$-direction; but cosine is now 1 unit “backwards”. We can add a negative sign to indicate that: $\sin(0^\circ)=0$ and $\cos(0^\circ)=-1$.
We will have to measure more or possibly derive/prove some more. In general, we can memorise a few “clean” angles and rely on a calculator or computer for all others. A few “clean” angles are:1