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

The general solution for sqrt(2)sin(3x)-1=0 is x= pi/(12)+(2pin)/3 ,x= pi/4+(2pin)/3

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sqrt(2)sin(3x)-1=0

2 sin (3 x) - 1 = 0

x = \frac{π}{12} + \frac{2 πn}{3}, x = \frac{π}{4} + \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{2}{2}

General solutions for

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

3 x = \frac{π}{4} + 2 πn, 3 x = \frac{3 π}{4} + 2 πn

Solve

3 x = \frac{π}{4} + 2 πn : x = \frac{π}{12} + \frac{2 πn}{3}

Solve

3 x = \frac{3 π}{4} + 2 πn : x = \frac{π}{4} + \frac{2 πn}{3}

x = \frac{π}{12} + \frac{2 πn}{3}, x = \frac{π}{4} + \frac{2 πn}{3}

4 cos (x + \frac{π}{4}) = - 1

cos (x) = \frac{3}{25}

csc (θ) + 3.35 = 0

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

y, 5^{2 x} - sin (y) = x

What is the general solution for sqrt(2)sin(3x)-1=0 ?
The general solution for sqrt(2)sin(3x)-1=0 is x= pi/(12)+(2pin)/3 ,x= pi/4+(2pin)/3