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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- Scegliere un'opzione
- Esprimere in termini di seno e coseno
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- Semplificare in un'unica funzione
- Esprimere in termini di seno
- Esprimere in termini di coseno
- Esprimere in termini di tangente
- Esprimere in termini di Cotangente
- Esprimere in termini di secante
- Esprimere in termini di Cosecante
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1
Apply the formula: $x+a=b$$\to x=b-a$, where $a=\frac{-\sqrt{2}}{2}$, $b=0$, $x+a=b=\sin\left(x\right)+\frac{-\sqrt{2}}{2}=0$, $x=\sin\left(x\right)$ and $x+a=\sin\left(x\right)+\frac{-\sqrt{2}}{2}$
$\sin\left(x\right)=- \frac{-\sqrt{2}}{2}$
2
Apply the formula: $-\frac{b}{c}$$=\frac{expand\left(-b\right)}{c}$, where $b=-\sqrt{2}$ and $c=2$
$\sin\left(x\right)=\frac{\sqrt{2}}{2}$
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
$x=\frac{1}{4}\pi+2\pi n,\:x=\frac{3}{4}\pi+2\pi n\:,\:\:n\in\Z$
