What is the general solution for |sin(x)|= 1/2 ?

The general solution for |sin(x)|= 1/2 is x=(7pi)/6+2pin,x=(11pi)/6+2pin,x= pi/6+2pin,x=(5pi)/6+2pin

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|sin(x)|= 1/2

∣ sin (x) ∣ = \frac{1}{2}

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

∣ sin (x) ∣ = \frac{1}{2}

Solve by substitution

sin (x) = - \frac{1}{2} or sin (x) = \frac{1}{2}

sin (x) = - \frac{1}{2} : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Combine all the solutions

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

sec^{2} (θ) = 2 tan (θ)

2 sin (2 x) + 2 = 0

2 cos^{2} (θ) - 3 sin (θ) + 2 = 0

sin (x) + sin (2 x) + sin (3 x) = 0

sin^{2} (x) - cos^{2} (x) = 1 + cos (x)

What is the general solution for |sin(x)|= 1/2 ?
The general solution for |sin(x)|= 1/2 is x=(7pi)/6+2pin,x=(11pi)/6+2pin,x= pi/6+2pin,x=(5pi)/6+2pin