Final Answer
$x=\frac{1}{4}\pi+2\pi n,\:x=\frac{3}{4}\pi+2\pi n\:,\:\:n\in\Z$
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Step-by-step Solution
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1
Calculate the square root of $2$
$\sin\left(x\right)+\frac{-\sqrt{2}}{2}=0$
2
Multiply $-1$ times $\sqrt{2}$
$\sin\left(x\right)-\frac{\sqrt{2}}{2}=0$
3
Divide $-\sqrt{2}$ by $2$
$\sin\left(x\right)-\frac{\sqrt{2}}{2}=0$
Intermediate steps
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
$\sin\left(x\right)=0+\frac{\sqrt{2}}{2}$
$x+0=x$, where $x$ is any expression
$\sin\left(x\right)=\frac{\sqrt{2}}{2}$
4
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
$\sin\left(x\right)=\frac{\sqrt{2}}{2}$
Explain more
5
The angles where the function $\sin\left(x\right)$ is $\frac{\sqrt{2}}{2}$ are
$x=45^{\circ}+360^{\circ}n,\:x=135^{\circ}+360^{\circ}n$
6
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
$x=\frac{1}{4}\pi+2\pi n,\:x=\frac{3}{4}\pi+2\pi n\:,\:\:n\in\Z$