## Solving sin x equations

“Sine” is a function, not a number. Sin (x) does not mean ‘sine times x’. New trig students often want to solve an equation like sin x = 0.5 by ‘dividing by sine’. This would be like solving

$\sqrt{x}=6 \text{ as } x= \dfrac{6}{\sqrt{\text{ }}}$

It’s completely meaningless! Instead, you need to take the inverse sine of both sides:

$\sin x=0.5$

$\sin^{-1}$ $\sin x =$ $\sin^{-1}$ $0.5=30 \textdegree$

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