What is the general solution for 2sin(3x)-1=0 ?

The general solution for 2sin(3x)-1=0 is x= pi/(18)+(2pin)/3 ,x=(5pi}{18}+\frac{2pin)/3

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2sin(3x)-1=0

2 sin (3 x) - 1 = 0

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

Solution steps

2 sin (3 x) - 1 = 0

Move

1

to the right side

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}

2 sin^{2} (x) - 3 sin (x) + 1 = 0

3 sin (\frac{π}{4})

tan (- \frac{13 π}{3})

2 cos^{2} (x) - sin (x) - 1 = 0

tan (\frac{π}{12})

What is the general solution for 2sin(3x)-1=0 ?
The general solution for 2sin(3x)-1=0 is x= pi/(18)+(2pin)/3 ,x=(5pi}{18}+\frac{2pin)/3