Final answer to the problem
$x=\frac{1}{4}\pi+2\pi n,\:x=\frac{3}{4}\pi+2\pi n\:,\:\:n\in\Z$
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Step-by-step Solution
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- Express in terms of sine and cosine
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- Express in terms of Sine
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1
We need to isolate the dependent variable $x$, we can do that by simultaneously subtracting $\frac{-\sqrt{2}}{2}$ from both sides of the equation
$\sin\left(x\right)=- \frac{-\sqrt{2}}{2}$
2
Multiplying the fraction by $-1$
$\sin\left(x\right)=\frac{\sqrt{2}}{2}$
3
The angles where the function $\sin\left(x\right)$ is $0$ are
$x=45^{\circ}+360^{\circ}n,\:x=135^{\circ}+360^{\circ}n$
4
The angles expressed in radians in the same order are equal to
$x=\frac{1}{4}\pi+2\pi n,\:x=\frac{3}{4}\pi+2\pi n\:,\:\:n\in\Z$
Final answer to the problem
$x=\frac{1}{4}\pi+2\pi n,\:x=\frac{3}{4}\pi+2\pi n\:,\:\:n\in\Z$
