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

The general solution for sin(2x)=(-sqrt(2))/2 is x=(5pi)/8+pin,x=(7pi)/8+pin

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

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

x = \frac{5 π}{8} + πn, x = \frac{7 π}{8} + πn

Solution steps

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

Apply the fraction rule:

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

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

General solutions for

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

2 x = \frac{5 π}{4} + 2 πn, 2 x = \frac{7 π}{4} + 2 πn

Solve

2 x = \frac{5 π}{4} + 2 πn : x = \frac{5 π}{8} + πn

Solve

2 x = \frac{7 π}{4} + 2 πn : x = \frac{7 π}{8} + πn

x = \frac{5 π}{8} + πn, x = \frac{7 π}{8} + πn

1 - cos^{2} (x) = 2 cos (x) + 2

7 tan (θ) = 23 + tan (θ)

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

24 tan^{2} (x) - 8 = 0

2 sin (x - \frac{π}{3}) = 1

What is the general solution for sin(2x)=(-sqrt(2))/2 ?
The general solution for sin(2x)=(-sqrt(2))/2 is x=(5pi)/8+pin,x=(7pi)/8+pin