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

The general solution for sin(3x)=(-1)/2 is x=(7pi}{18}+(2pin)/3 ,x=(11pi)/(18)+\frac{2pin)/3

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

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

x = \frac{7 π}{18} + \frac{2 πn}{3}, x = \frac{11 π}{18} + \frac{2 πn}{3}

Solution steps

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

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

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

General solutions for

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

3 x = \frac{7 π}{6} + 2 πn, 3 x = \frac{11 π}{6} + 2 πn

Solve

3 x = \frac{7 π}{6} + 2 πn : x = \frac{7 π}{18} + \frac{2 πn}{3}

Solve

3 x = \frac{11 π}{6} + 2 πn : x = \frac{11 π}{18} + \frac{2 πn}{3}

x = \frac{7 π}{18} + \frac{2 πn}{3}, x = \frac{11 π}{18} + \frac{2 πn}{3}

4 cos^{2} (x) + 7 sin (x) - 2 = 0

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

sin (5 θ) = 0

tanh (x) = 0

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

What is the general solution for sin(3x)=(-1)/2 ?
The general solution for sin(3x)=(-1)/2 is x=(7pi}{18}+(2pin)/3 ,x=(11pi)/(18)+\frac{2pin)/3