Question

Sa se rezolve ecuatia: sin ( pi/4-x) = 1/2 .

Answer 1

sin (pi/4-x)=sin 30
pi/4-x=30
45-30=x
x=15

Answer 2

   
[tex]\displaystyle \\ \sin ( \frac{\pi}{4} -x) = 1/2 \\ \\ \texttt{Avem 2 solutii: } \\ \\ \texttt{Solutia 1: } \\ \\ \frac{\pi}{4} -x = \frac{\pi}{6} + 2k\pi \\ \\ x_{_1} = \frac{\pi}{4}-\frac{\pi}{6} -2k\pi = \frac{3\pi-2\pi}{12}-2k\pi= \boxed{\frac{\pi}{12}-2k\pi} \\ \\ \\ \texttt{Solutia 2: } \\ \\ \frac{\pi}{4} -x = \frac{5\pi}{6} + 2k\pi \\ \\ x_{_2} = \frac{\pi}{4}-\frac{5\pi}{6} -2k\pi = \frac{3\pi-10\pi}{12}-2k\pi= \boxed{-\frac{7\pi}{12}-2k\pi} [/tex]