Solve the trigonometric equation 4sin(x)=2sin(x)+2^(1/2)

 Exercise

$4\sin\left(x\right)=2\sin\left(x\right)+\sqrt{2}$

 

Group the terms of the equation by moving the terms that have the variable $x$ to the left side, and those that do not have it to the right side

$4\sin\left(x\right)-2\sin\left(x\right)=\sqrt{2}$

 

Combining like terms $4\sin\left(x\right)$ and $-2\sin\left(x\right)$

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

 

Divide both sides of the equation by $2$

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

 

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

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

 

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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