Тригонометрические уравнения
\(\sin{x}=-1\) \(\Leftrightarrow\) \(x=-\displaystyle\frac{\pi}{2}+2\pi n\), \(n\in Z\)
\(\sin{x}=0\) \(\Leftrightarrow\) \(x=\pi n\), \(n\in Z\)
\(\sin{x}=1\) \(\Leftrightarrow\) \(x=\displaystyle\frac{\pi}{2}+2\pi n\), \(n\in Z\)
\(\cos{x}=-1\) \(\Leftrightarrow\) \(x=\pi+2\pi n\), \(n\in Z\)
\(\cos{x}=0\) \(\Leftrightarrow\) \(x=\displaystyle\frac{\pi}{2}+\pi n\), \(n\in Z\)
\(\cos{x}=1\) \(\Leftrightarrow\) \(x=2\pi n\), \(n\in Z\)
\(\sin{x}=a\), \(-1\le a\le 1\) \(\Leftrightarrow\) \(x=(-1)^n\arcsin{a}+\pi n\), \(n\in Z\)
\(\cos{x}=a\), \(-1\le a\le 1\) \(\Leftrightarrow\) \(x=\pm\arccos{a}+2\pi n\), \(n\in Z\)
\(\mathrm{tg}{x}=a\) \(\Leftrightarrow\) \(x=\mathrm{arctg}{a}+\pi n\), \(n\in Z\)
\(\mathrm{ctg}{x}=a\) \(\Leftrightarrow\) \(x=\mathrm{arcctg}{a}+\pi n\), \(n\in Z\)
\(\sin{x}=\sin{y}\) \(\Leftrightarrow\) \(\left[\begin{array}{l l} x=y+2\pi n, n\in Z \\ x=\pi-y+2\pi n, n\in Z\end{array}\right. \)
\(\cos{x}=\cos{y}\) \(\Leftrightarrow\) \(\left[\begin{array}{l l} x=y+2\pi n, n\in Z \\ x=-y+2\pi n, n\in Z\end{array}\right. \)
\(\mathrm{tg}{x}=\mathrm{tg}{y}\) \(\Leftrightarrow\) \(x=y+\pi n, n\in Z \)
\(\mathrm{ctg}{x}=\mathrm{ctg}{y}\) \(\Leftrightarrow\) \(x=y+\pi n, n\in Z \)