What is the general solution for sin(3θ)= 1/2 ?

The general solution for sin(3θ)= 1/2 is θ= pi/(18)+(2pin)/3 ,θ=(5pi}{18}+\frac{2pin)/3

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sin(3θ)= 1/2

sin (3 θ) = \frac{1}{2}

θ = \frac{π}{18} + \frac{2 πn}{3}, θ = \frac{5 π}{18} + \frac{2 πn}{3}

Solution steps

sin (3 θ) = \frac{1}{2}

General solutions for

sin (3 θ) = \frac{1}{2}

3 θ = \frac{π}{6} + 2 πn, 3 θ = \frac{5 π}{6} + 2 πn

Solve

3 θ = \frac{π}{6} + 2 πn : θ = \frac{π}{18} + \frac{2 πn}{3}

Solve

3 θ = \frac{5 π}{6} + 2 πn : θ = \frac{5 π}{18} + \frac{2 πn}{3}

θ = \frac{π}{18} + \frac{2 πn}{3}, θ = \frac{5 π}{18} + \frac{2 πn}{3}

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

1 - sin (θ) = 2 cos^{2} (θ)

2 sin^{2} (θ) - 3 sin (θ) = 0

sec^{2} (x) + 2 tan (x) = 4

tan (\frac{x}{5}) + 3 = 0

What is the general solution for sin(3θ)= 1/2 ?
The general solution for sin(3θ)= 1/2 is θ= pi/(18)+(2pin)/3 ,θ=(5pi}{18}+\frac{2pin)/3