Question

Giải phương trình sau: sinx=1/2

Answer 1

Answer:

$x = \frac{\pi}{6} +2\pi k \space , \space \text{for any integer values of } k$

$x = \frac{5\pi}{6} -2\pi k \space , \space \text{for any integer values of } k$

Step-by-step explanation:

Solving with the Periodicity Identity:

$\sin(x)= \frac{1}{2} \\ x = \arcsin(\frac{1}{2}) +2\pi k \\ x = \frac{\pi}{6} +2\pi k$

Solving with the Symmetry Identity:

$\sin(x) = \frac{1}{2} \\ \sin(\pi -x) = \frac{1}{2} \\ \pi -x = \arcsin(\frac{1}{2}) +2\pi k \\ \pi -x = \frac{\pi}{6} +2\pi k \\ -x = \frac{\pi}{6} +2\pi k -\pi \\ -x = \frac{\pi}{6} - \frac{6\pi}{6} +2\pi k \\ -x = -\frac{5\pi}{6} + 2\pi k \\ x = \frac{5\pi}{6} -2\pi k$

Answer 2

Answer: $\begin{bmatrix}\mathrm{Radians:}\:&\:x=\frac{\pi }{6}+2\pi n,\:x=\frac{5\pi }{6}+2\pi n\:\\ \:\mathrm{Degrees:}&\:x=30^{\circ \:}+360^{\circ \:}n,\:x=150^{\circ \:}+360^{\circ \:}n\end{bmatrix}$

Step-by-step explanation:

$\sin \left(x\right)=\frac{1}{2}$

$x=\frac{\pi }{6}+2\pi n,\:x=\frac{5\pi }{6}+2\pi$