Question

How do you solve $\sin \left(x\right)=0.5$?

Answer 1

Solve for the required value:

Given that, $\sin \left(x\right)=0.5$

$$\begin{gathered} \sin \left(x\right)=0.5 \\ \Rightarrow \sin \left(x\right)=\frac{1}{2} \\ \Rightarrow \sin \left(x\right)=\sin (30°)or\sin \left(\frac{\pi }{6}\right) \\ \therefore x=30°or\frac{\pi }{6} \end{gathered}$$

General solution of

$$\begin{gathered} \sin \alpha =\sin \beta \\ \Rightarrow \alpha =n\mathrm{\pi }+{(-1)}^{\mathrm{n}}\mathrm{\beta } \end{gathered}$$

$\therefore$$x=n\mathrm{\pi }+{(-1)}^{\mathrm{n}}\frac{\mathrm{\pi }}{6}$

Hence, the value of $x$ is $30°$ or $\frac{\mathrm{\pi }}{6}$and general solution is $x=n\mathrm{\pi }+{(-1)}^{\mathrm{n}}\frac{\mathrm{\pi }}{6}$.