Równanie trygonometryczne
: 14 mar 2021, 09:33
Rozwiąż równanie.
\(\sin(x+ \frac{1}{4} \pi )\cos(x+ \frac{1}{4} \pi )= \frac{ \sqrt{2} }{4}\)
\(\sin(x+ \frac{1}{4} \pi )\cos(x+ \frac{1}{4} \pi )= \frac{ \sqrt{2} }{4}\)
\(\frac{1}{2}\sin (2x+\frac{\pi}{2})=\frac{\sqrt{2}}{4}\\Januszgolenia pisze: ↑14 mar 2021, 09:33 Rozwiąż równanie.
\(sin(x+ \frac{1}{4} \pi )cos(x+ \frac{1}{4} \pi )= \frac{ \sqrt{2} }{4}\)
\sin (2x+\frac{\pi}{2})=\frac{\sqrt{2}}{2}\\
2x+\frac{\pi}{2}=\frac{\pi}{4}+2k\pi\;\;\;\vee\;\;\;2x+\frac{\pi}{2}=\frac{3\pi}{4}+2k\pi\\
x=-\frac{\pi}{8}+k\pi\;\;\;\vee\;\;\;x=\frac{\pi}{8}+k\pi, k\in\mathbb{C}\)