# Solve the equation 3+sin theta=frac{6-sqrt{2}}{2}

Solve the equation $3+\mathrm{sin}\theta =\frac{6-\sqrt{2}}{2}$
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Separate the right side
$3+\mathrm{sin}\theta =3-\frac{\sqrt{2}}{2}$
Substruct 3 from both sides
$\mathrm{sin}\theta =-\frac{\sqrt{2}}{2}$
The reference angle is ${\theta }^{\prime }=45°$ since $45°=\frac{\sqrt{2}}{2}$. Recall that sine is negative on QIII and QIV.
The QIII solution is
$\theta =180°+{\theta }^{\prime }=180°+45°$
$\theta =225°$
The QIV solution is
$\theta =360°-{\theta }^{\prime }=360°-45°$
$\theta =315$°