Kunnskapsgnist
Trigonometriske identiteter er noen sammenhenger som gjør det enklere å regne med sinus og cosinus.
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)
$$\begin{aligned} \sin \left( v + \frac{\pi}{2}\right) &= \cos(v) \\ \cos \left( v + \frac{\pi}{2}\right) &= - \sin(v) \end{aligned}$$
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