What is the general solution for sin(4θ)=-1/2 ?

The general solution for sin(4θ)=-1/2 is θ=(7pi}{24}+(pin)/2 ,θ=(11pi)/(24)+\frac{pin)/2

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sin(4θ)=-1/2

sin (4 θ) = - \frac{1}{2}

θ = \frac{7 π}{24} + \frac{πn}{2}, θ = \frac{11 π}{24} + \frac{πn}{2}

Solution steps

sin (4 θ) = - \frac{1}{2}

General solutions for

sin (4 θ) = - \frac{1}{2}

4 θ = \frac{7 π}{6} + 2 πn, 4 θ = \frac{11 π}{6} + 2 πn

Solve

4 θ = \frac{7 π}{6} + 2 πn : θ = \frac{7 π}{24} + \frac{πn}{2}

Solve

4 θ = \frac{11 π}{6} + 2 πn : θ = \frac{11 π}{24} + \frac{πn}{2}

θ = \frac{7 π}{24} + \frac{πn}{2}, θ = \frac{11 π}{24} + \frac{πn}{2}

cos (x) = \frac{3}{4}

cos^{2} (x) + \frac{3}{2} sin (2 x) = 0

7 cos (2 x) = 7 cos (x)

csc (\frac{θ}{3}) = \frac{2 3}{3}

3 tan (θ) - cot (θ) = 0

What is the general solution for sin(4θ)=-1/2 ?
The general solution for sin(4θ)=-1/2 is θ=(7pi}{24}+(pin)/2 ,θ=(11pi)/(24)+\frac{pin)/2