Jaeden Frederick

2022-01-25

I cannot find how or why this,
$5\mathrm{sin}3x-1=3$
Has one of two solutions being this,
$42.99+n×{120}^{\circ }$
I am lost on how to get this solution. I have found the other one, so I will not mention it.

Emilie Booker

Expert

Note that $\mathrm{sin}3x=\mathrm{sin}\left({180}^{\circ }-3x\right)=45={\mathrm{sin}53.1}^{\circ }$, which gives two sets of solutions,
$3x={53.1}^{\circ }+n{360}^{\circ }$
$3x={\left(180-53.1\right)}^{\circ }+n{360}^{\circ }$
with n being integers. Thus, the complete sultions are

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