Divide both sides by 4
sin(2x+30)=−2/4
2
Simplify \frac{2}{4}42 to \frac{1}{2}21
\sin{(2x+30)}=-\frac{1}{2}sin(2x+30)=−21
Ask: What values of 2x+302x+30 will make \sin{(2x+30)}sin(2x+30) equal -\frac{1}{2}−21?
2x+30=-\frac{\pi }{6},-\frac{5\pi }{6}2x+30=−6π,−65π
Since sin is a periodic function, add the periodicity
2x+30=2\pi n-\frac{\pi }{6},n \in Z2x+30=2πn−6π,n∈Z
2x+30=2\pi n-\frac{5\pi }{6},n \in Z2x+30=2πn−65π,n∈Z
5
Solve for x
x=πn−12π−15,n∈Z
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x=πn-π/12-15,n∈Z
x=πn-π/12-15,n∈Z
