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

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

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sqrt(2)sin(3x)=1

2 sin (3 x) = 1

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

Solution steps

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}

sin (4 x) = cos (2 x)

cot^{2} (θ) - cot (θ) = 0

5 cos (2 θ) = - 15 cos (θ) - 10

2 cos (x) - 5 = 3 sec (x)

sin (3 θ + \frac{π}{18}) = 1, 0 \leq θ < 2 π

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