solving for x(trig)

Divide both sides by 4

sin(2x+30)=−​2/4

2

 

Simplify \frac{2}{4}​4​​2​​ to \frac{1}{2}​2​​1​​

\sin{(2x+30)}=-\frac{1}{2}sin(2x+30)=−​2​​1​​

Ask: What values of 2x+302x+30 will make \sin{(2x+30)}sin(2x+30) equal -\frac{1}{2}−​2​​1​​?

2x+30=-\frac{\pi }{6},-\frac{5\pi }{6}2x+30=−​6​​π​​,−​6​​5π​​

Since sin is a periodic function, add the periodicity

2x+30=2\pi n-\frac{\pi }{6},n \in Z2x+30=2πn−​6​​π​​,n∈Z
2x+30=2\pi n-\frac{5\pi }{6},n \in Z2x+30=2πn−​6​​5π​​,n∈Z

5

 

Solve for x

x=πn−​12​​π​​−15,n∈Z

 

=====================
x=πn-​π​​/12-15,n∈Z

x=πn-​π​​/12-15,n∈Z

\(4\sin(2x+30^{\circ})=-2\\ \sin(2x + 30^{\circ}) = -\dfrac{1}{2}\\ 2x + 30^{\circ} =\arcsin (-\dfrac{1}{2})\\ 2x + 30^{\circ} = -30^{\circ}\\ 2x = -60^{\circ}\\ x = 360^{\circ}n-30^{\circ}\text{ OR }360^{\circ}n+210^{\circ}\)

.