Step-by-step Solution

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

Go!
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Final Answer

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

Step-by-step Solution

Problem to solve:

$sin\left(x\right)-\frac{\sqrt{2}}{2}=0$
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We need to isolate the dependent variable $x$, we can do that by subtracting $-\frac{\sqrt{2}}{2}$ from both sides of the equation

$\sin\left(x\right)=\frac{\sqrt{2}}{2}$
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The angles where the function $\sin\left(x\right)$ is $\frac{\sqrt{2}}{2}$ are

$x=45^{\circ}+360^{\circ}n,\:x=135^{\circ}+360^{\circ}n$
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The angles expressed in radians in the same order are equal to

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

Final Answer

$x=\frac{1}{4}\pi+2\pi n,\:x=\frac{3}{4}\pi+2\pi n$
$sin\left(x\right)-\frac{\sqrt{2}}{2}=0$

Time to solve it:

~ 0.03 s

Related topics:

Trigonometric Equations