Určení periody funkce
Urči periodu zadané funkce:
\( \large f\left( x\right) = \cos \left( 2x+\Large \frac{\pi}{2}\large \right) \)
\( 2x\ +\ \frac{\pi}{2}\ +\ 2k \pi = 2(x\ +\ k \cdot p)\ +\ \frac{\pi}{2} \)
\( 2x\ +\ \frac{\pi}{2}\ +\ 2k\pi = 2x\ +\ 2kp\ +\ \frac{\pi}{2} \)
\( 2 \pi = 2p \)
\( p = \pi \)
\( 2x\ +\ \frac{\pi}{2}\ +\ 2k \pi = 2(x\ +\ k \cdot p)\ +\ \frac{\pi}{3} \)
\( 2x\ +\ \frac{\pi}{2}\ +\ 2k\pi = 2x\ +\ 2kp\ +\ \frac{\pi}{3} \)
\( 2 \pi = 3p \)
\( p = \frac{2\pi}{3} \)
\( 2x\ +\ \frac{\pi}{2}\ +\ 2k \pi = 2(x\ +\ k \cdot p)\ +\ \frac{\pi}{6} \)
\( 2x\ +\ \frac{\pi}{2}\ +\ 2k\pi = 2x\ +\ 2kp\ +\ \frac{\pi}{6} \)
\( 2 \pi = 6p \)
\( p = \frac{\pi}{3} \)
\( 2x\ +\ \frac{\pi}{2}\ +\ 2k \pi = 2(x\ +\ k \cdot p)\ +\ \frac{\pi}{4} \)
\( 2x\ +\ \frac{\pi}{2}\ +\ 2k\pi = 2x\ +\ 2kp\ +\ \frac{\pi}{4} \)
\( 2 \pi = 4p \)
\( p = \frac{\pi}{2} \)