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