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

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

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2sin(3x)=1

2 sin (3 x) = 1

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

Solution steps

2 sin (3 x) = 1

Divide both sides by

2

sin (3 x) = \frac{1}{2}

General solutions for

sin (3 x) = \frac{1}{2}

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

Solve

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

Solve

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

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

cos (θ) - sin (θ) = 1

sin^{2} (x) - cos^{2} (x) + sin (x) = 0

3 cot^{2} (x) = 1

cos (θ) = - \frac{5}{13}

4 sec (θ) + 6 = - 2

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