Question

Buna ziua cum as putea rezolva aceasta problema: determinati solutiile ecuatiei sinx=1/2, ce apartine multimii[0, 2pi]?

Answer 1

   
$\displaystyle\\ \sin x= \frac{1}{2}\\\\ \text{Formula generala: }\\\\ \begin{cases}x_1 = \arcsin \dfrac{1}{2} + 2k\pi,\\\\x_2 = \pi - \arcsin \dfrac{1}{2} + 2pk\end{cases},\;{k}\in{\mathbb{R}}\\\\ \text{Rezolvarea pentru }~~x\in [0;~ 2\pi]\\\\ \begin{cases}x_1 = \arcsin\dfrac{1}{2}=\dfrac{\pi}{6} = 30^o\\\\ x_2 =\pi-\arcsin\dfrac{1}{2}= \pi - \dfrac{\pi}{6} = \dfrac{5\pi}{6} = 150^o \end{cases}$