Teresa Manning

2023-03-11

The principal solution of the equation $\mathrm{sin}x=1/2$ that is less than $\frac{\pi}{2}$ is

A)$\frac{\pi}{3}$

B)$\frac{\pi}{2}$

C)$\frac{\pi}{6}$

A)$\frac{\pi}{3}$

B)$\frac{\pi}{2}$

C)$\frac{\pi}{6}$

fodheargnl0

Beginner2023-03-12Added 4 answers

The right answer is C $\frac{\pi}{6}$

We have equation is:

$\mathrm{sin}x=\frac{1}{2}$

$\Rightarrow \mathrm{sin}x=\mathrm{sin}\frac{\pi}{6}$

Hence, one principal solution of the equation is $\frac{\pi}{6}$

Also, $\mathrm{sin}x=\mathrm{sin}(\pi -x)$

Hence, $\mathrm{sin}\frac{\pi}{6}=\mathrm{sin}(\pi -\frac{\pi}{6})$

Or, $\mathrm{sin}\frac{\pi}{6}=\mathrm{sin}\frac{5\pi}{6}$

Therefore, the other main answer to the equation is $\frac{5\pi}{6}$.

The principal solution which is less than $\frac{\pi}{2}$ is $\frac{\pi}{6}$

We have equation is:

$\mathrm{sin}x=\frac{1}{2}$

$\Rightarrow \mathrm{sin}x=\mathrm{sin}\frac{\pi}{6}$

Hence, one principal solution of the equation is $\frac{\pi}{6}$

Also, $\mathrm{sin}x=\mathrm{sin}(\pi -x)$

Hence, $\mathrm{sin}\frac{\pi}{6}=\mathrm{sin}(\pi -\frac{\pi}{6})$

Or, $\mathrm{sin}\frac{\pi}{6}=\mathrm{sin}\frac{5\pi}{6}$

Therefore, the other main answer to the equation is $\frac{5\pi}{6}$.

The principal solution which is less than $\frac{\pi}{2}$ is $\frac{\pi}{6}$