### Teorija

Vienādojuma tgx = a un ctgx = a atrisinājums
Vienādojumam tgx = a un ctgx = a ir atrisinājums ar jebkuru reālu a vērtību, atšķirībā no sinx un cosx, kuru vērtību apgabals ir [-1;1]

1) Ja tgx = a,  tad $x=\mathit{arctga}+{180}^{o}n\phantom{\rule{0.735em}{0ex}}\mathit{jeb}\phantom{\rule{0.735em}{0ex}}x=\mathit{arctga}+\mathrm{\pi }n,\phantom{\rule{0.441em}{0ex}}\mathit{kur}\phantom{\rule{0.147em}{0ex}}n\in Z$

Iegaumē:
arctg(-a) = -arctga

Tātad, ja tgx = - a , tad $x=-\mathit{arctga}+{180}^{o}n\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\mathit{jeb}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}x=-\mathit{arctga}+\mathrm{\pi }n,\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\mathit{kur}\phantom{\rule{0.147em}{0ex}}n\in Z$

2) Ja ctgx = a,  tad $x=\mathit{arcctga}+{180}^{o}n\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\mathit{jeb}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}x=\mathit{arcctga}+\mathrm{\pi }n,\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\mathit{kur}\phantom{\rule{0.147em}{0ex}}n\in Z$

Iegaumē:
arcctg(-a) =${180}^{o}$-arcctga

Tātad, ja ctgx = - a , tad $x=\mathit{180}\mathrm{°}-\mathit{arcctga}+{180}^{o}n\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\mathit{jeb}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}x=\mathrm{\pi }-\mathit{arcctga}+\mathrm{\pi }n,\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\mathit{kur}\phantom{\rule{0.147em}{0ex}}n\in Z$

Izpēti tabulu!

Trigonometrisko funkciju salīdzinājums
 Funkcija Vērtību apgabals  (a vērtības) Definīcijas apgabals (pieļaujamās x vērtības) sinx,  cosx [-1;1] $\left(-\mathrm{\infty };+\mathrm{\infty }\right)$ tgx $\left(-\mathrm{\infty };+\mathrm{\infty }\right)$ $\begin{array}{l}x\ne {90}^{o}+{180}^{o}n\\ \mathit{jeb}\\ x\ne \frac{\mathrm{\pi }}{2}+\mathrm{\pi }n,\phantom{\rule{0.147em}{0ex}}\mathit{kur}\phantom{\rule{0.147em}{0ex}}n\in Z\end{array}$ ctgx $\left(-\mathrm{\infty };+\mathrm{\infty }\right)$ $\begin{array}{l}x\ne {180}^{o}n\\ \mathit{jeb}\\ x\ne \mathrm{\pi }n,\phantom{\rule{0.147em}{0ex}}\mathit{kur}\phantom{\rule{0.147em}{0ex}}n\in Z\end{array}$

Piemērs:
$\begin{array}{l}\mathit{ctgx}=-1\\ x={180}^{o}-{45}^{o}+{180}^{o}n\phantom{\rule{0.441em}{0ex}}x={135}^{o}+{180}^{o}n\phantom{\rule{0.147em}{0ex}},\phantom{\rule{0.147em}{0ex}}\mathit{kur}\phantom{\rule{0.147em}{0ex}}n\in Z\\ \end{array}$

Piemērs:
$\begin{array}{l}\mathit{tg}\frac{x}{2}=14\phantom{\rule{0.735em}{0ex}}\\ \frac{x}{2}=\mathit{arctg14}+\mathrm{\pi }n\phantom{\rule{0.882em}{0ex}}\left|\cdot 2\right\\ \phantom{\rule{1.029em}{0ex}}\\ x=2\cdot \mathit{arctg14}+2\mathrm{\pi }n,\phantom{\rule{0.147em}{0ex}}\mathit{kur}\phantom{\rule{0.147em}{0ex}}n\in Z\end{array}$