Rovnica cotg:5x=0
Vyrieš v ℝ rovnicu:
\( \normalsize cotg\:5x=0 \)
\( 5x = r \)
\( 5x = \frac{\pi}{4} + k \pi;\ k \in \mathbb{Z} \)
\( x = \frac{\pi}{20} + \frac{k \pi}{5};\ k \in \mathbb{Z} \)
\( \normalsize K=\bigcup\limits_{k\in\mathbb{Z}}\left\{\frac{\pi}{{20}}+\frac{k\pi}{5}\right\} \)
\( 5x = r \)
\( 5x = \pi + k \pi;\ k \in \mathbb{Z} \)
\( x = \frac{\pi}{5} + \frac{k \pi}{5};\ k \in \mathbb{Z} \)
\( \normalsize K=\bigcup\limits_{k\in\mathbb{Z}}\left\{\frac{\pi}{{5}}+\frac{k\pi}{5}\right\} \)
\( 5x = r \)
\( 5x = \frac{\pi}{2} + k \pi;\ k \in \mathbb{Z} \)
\( x = \frac{\pi}{10} + \frac{k \pi}{5};\ k \in \mathbb{Z} \)
\( \normalsize K=\bigcup\limits_{k\in\mathbb{Z}}\left\{\frac{\pi}{{10}}+\frac{k\pi}{5}\right\} \)
\( 5x = r \)
\( 5x = \frac{\pi}{3} + k \pi;\ k \in \mathbb{Z} \)
\( x = \frac{\pi}{15} + \frac{k \pi}{5};\ k \in \mathbb{Z} \)
\( \normalsize K=\bigcup\limits_{k\in\mathbb{Z}}\left\{\frac{\pi}{{15}}+\frac{k\pi}{5}\right\} \)
Rovnica obsahuje v argumente päťnásobný uhol. Takže ho musíš nahradiť niečím iným.
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