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