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

The general solution for sin(2x)=(-1)/2 is x=(7pi)/(12)+pin,x=(11pi)/(12)+pin

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

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

x = \frac{7 π}{12} + πn, x = \frac{11 π}{12} + πn

Solution steps

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

Apply the fraction rule:

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

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

General solutions for

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

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

Solve

2 x = \frac{7 π}{6} + 2 πn : x = \frac{7 π}{12} + πn

Solve

2 x = \frac{11 π}{6} + 2 πn : x = \frac{11 π}{12} + πn

x = \frac{7 π}{12} + πn, x = \frac{11 π}{12} + πn

csc (2 x) + 1 = 0

cos (5 x) - cos (x) = sin (3 x)

1 = cos (\frac{( π ( t - 22 ) )}{183})

cot (x) = - csc^{2} (x)

3 cos^{2} (θ) + 4 cos (θ) - 4 = 0

What is the general solution for sin(2x)=(-1)/2 ?
The general solution for sin(2x)=(-1)/2 is x=(7pi)/(12)+pin,x=(11pi)/(12)+pin