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

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

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sin(3x)= 1/(sqrt(2))

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

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

Solution steps

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

Simplify

\frac{1}{2} : \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}

tan^{2} (θ) = - tan (θ)

sec (θ) = - \frac{2}{3}

tan (θ) = \frac{8}{12}

sin (t) + cos (t) = 0

0 = cos (3 x)

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