Řešení rovnice cotg5x = 0
Vyřeš v \( \R \) rovnici:
\( \large \text{cotg}5x = 0 \)
\( 5x = r \)
\( 5x = \frac{\pi}{4} + k \pi;\ k \in \mathbb{Z} \)
\( x = \frac{\pi}{20} + \frac{k \pi}{5};\ k \in \mathbb{Z} \)
\( K = \bigcup_\limits{k\ \in\ \mathbb{Z}} \left \{\frac{\pi}{{20}} + \frac{k \pi}{5}\right\} \)
\( 5x = r \)
\( 5x = \frac{3\pi}{2} + k \pi;\ k \in \mathbb{Z} \)
\( x = \frac{3\pi}{10} + \frac{k \pi}{5};\ k \in \mathbb{Z} \)
\( K = \bigcup_\limits{k\ \in\ \mathbb{Z}} \left \{\frac{3\pi}{{10}} + \frac{k \pi}{5}\right\} \)
\( 5x = r \)
\( 5x = \frac{\pi}{2} + k \pi;\ k \in \mathbb{Z} \)
\( x = \frac{\pi}{10} + \frac{k \pi}{5};\ k \in \mathbb{Z} \)
\( K = \bigcup_\limits{k\ \in\ \mathbb{Z}} \left \{\frac{\pi}{{10}} + \frac{k \pi}{5}\right\} \)
\( 5x = r \)
\( 5x = \pi + k \pi;\ k \in \mathbb{Z} \)
\( x = \frac{\pi}{5} + \frac{k \pi}{5};\ k \in \mathbb{Z} \)
\( K = \bigcup_\limits{k\ \in\ \mathbb{Z}} \left \{\frac{\pi}{{5}} + \frac{k \pi}{5}\right\} \)
Rovnice obsahuje v argumentu pětinásobný úhel. Takže ho musíš nahradit něčím jiným.