Caleb Proctor

2022-07-15

Find all values of x in the interval $\left[0,2\pi \right]$ that satisfy the equation:
$2{\mathrm{sin}}^{2}x=1$

SweallySnicles3

Expert

$2{\mathrm{sin}}^{2}x=1$
${\mathrm{sin}}^{2}x=\frac{1}{2}$
$\mathrm{sin}x=±\sqrt{\frac{1}{2}}$
$\mathrm{sin}x=±\frac{1}{\sqrt{2}}\ast \frac{\sqrt{2}}{\sqrt{2}}$
$\mathrm{sin}x=±\frac{\sqrt{2}}{2}$
$x=\frac{\pi }{4};\frac{7\pi }{4};\frac{3\pi }{4};\frac{5\pi }{4}$

Jeffrey Jordon

Expert