What is the general solution for 2sin(-3x-pi/4)=sqrt(2) ?

The general solution for 2sin(-3x-pi/4)=sqrt(2) is x=-pi/6-(2pin)/3 ,x=-(2pin)/3-pi/3

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2sin(-3x-pi/4)=sqrt(2)

2 sin (- 3 x - \frac{π}{4}) = 2

x = - \frac{π}{6} - \frac{2 πn}{3}, x = - \frac{2 πn}{3} - \frac{π}{3}

Solution steps

2 sin (- 3 x - \frac{π}{4}) = 2

Divide both sides by

2

sin (- 3 x - \frac{π}{4}) = \frac{2}{2}

General solutions for

sin (- 3 x - \frac{π}{4}) = \frac{2}{2}

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

Solve

- 3 x - \frac{π}{4} = \frac{π}{4} + 2 πn : x = - \frac{π}{6} - \frac{2 πn}{3}

Solve

- 3 x - \frac{π}{4} = \frac{3 π}{4} + 2 πn : x = - \frac{2 πn}{3} - \frac{π}{3}

x = - \frac{π}{6} - \frac{2 πn}{3}, x = - \frac{2 πn}{3} - \frac{π}{3}

4 sin^{3} (θ) - 3 sin (θ) = 0

\frac{sec ^{2} ( θ ) - 1}{1 - cos ^{2} ( θ )} - 1 = cot^{2} (θ)

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

4 cos (x) + 4 sin (x) tan (x) = 8

2 tan^{2} (x) - 3 sec (x) = 0

What is the general solution for 2sin(-3x-pi/4)=sqrt(2) ?
The general solution for 2sin(-3x-pi/4)=sqrt(2) is x=-pi/6-(2pin)/3 ,x=-(2pin)/3-pi/3