Solve the trigonometric equation sin(x)+(-*2^(1/2))/2=0

 Exercise

$sin\left(x\right)-\frac{\sqrt{2}}{2}=0$

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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

$\sin\left(x\right)=- \frac{-\sqrt{2}}{2}$

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Multiplying the fraction by $-1$

$\sin\left(x\right)=\frac{\sqrt{2}}{2}$

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The angles where the function $\sin\left(x\right)$ is $0$ are

$x=45^{\circ}+360^{\circ}n,\:x=135^{\circ}+360^{\circ}n$

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The angles expressed in radians in the same order are equal to

$x=\frac{1}{4}\pi+2\pi n,\:x=\frac{3}{4}\pi+2\pi n\:,\:\:n\in\Z$

$x=\frac{1}{4}\pi+2\pi n,\:x=\frac{3}{4}\pi+2\pi n\:,\:\:n\in\Z$

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