Enhetsformelen: (forklaring)
\cos^2 (v) + \sin^2 (v) = 1
Summen av to vinkler:
\sin(\textcolor{red}{u} + \textcolor{blue}{v}) = \sin(\textcolor{red}{u}) \cos(\textcolor{blue}{v}) + \sin(\textcolor{blue}{v}) \cos(\textcolor{red}{u}) \\
\cos(\textcolor{red}{u} + \textcolor{blue}{v}) = \cos(\textcolor{red}{u}) \cos(\textcolor{blue}{v}) - \sin(\textcolor{red}{u}) \sin(\textcolor{blue}{v}) \\
Negativ vinkel: (forklaring)
\begin{aligned}
\sin(-v) &= - \sin(v) \\
\cos(-v) &= \cos(v)
\end{aligned}Store vinkler: (forklaring)
\sin(v + 2n\pi) = \sin(v) \\ \cos(v + 2n\pi) = \cos(v)
der $n$ er heltall.
Sammenheng mellom sinus og cosinus: (forklaring)
\begin{aligned}
\sin \left( v + \frac{\pi}{2}\right) &= \cos(v) \\
\cos \left( v + \frac{\pi}{2}\right) &= - \sin(v)
\end{aligned}+ Doble vinkler
Sinus og cosinus til $2v$ kan vi finne ved å sette $u = v$ i formelen for summen av to vinkler:
\begin{array}{rcccl}
\sin(\textcolor{red}{v} + \textcolor{blue}{v}) &=& \sin(\textcolor{red}{v}) \cos(\textcolor{blue}{v}) + \sin(\textcolor{blue}{v}) \cos(\textcolor{red}{v}) &=& 2\sin(v)\cos(v) \\
\cos(\textcolor{red}{v} + \textcolor{blue}{v}) &=&\cos(\textcolor{red}{v}) \cos(\textcolor{blue}{v}) - \sin(\textcolor{red}{v}) \sin(\textcolor{blue}{v}) &=& \cos^2(v) - \sin^2(v)
\end{array}