What is the general solution for 2sin(3x)+sqrt(2)=0 ?

The general solution for 2sin(3x)+sqrt(2)=0 is x=(5pi}{12}+(2pin)/3 ,x=(7pi)/(12)+\frac{2pin)/3

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2sin(3x)+sqrt(2)=0

2 sin (3 x) + 2 = 0

x = \frac{5 π}{12} + \frac{2 πn}{3}, x = \frac{7 π}{12} + \frac{2 πn}{3}

Solution steps

2 sin (3 x) + 2 = 0

Move

2

to the right side

2 sin (3 x) = - 2

Divide both sides by

2

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

General solutions for

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

3 x = \frac{5 π}{4} + 2 πn, 3 x = \frac{7 π}{4} + 2 πn

Solve

3 x = \frac{5 π}{4} + 2 πn : x = \frac{5 π}{12} + \frac{2 πn}{3}

Solve

3 x = \frac{7 π}{4} + 2 πn : x = \frac{7 π}{12} + \frac{2 πn}{3}

x = \frac{5 π}{12} + \frac{2 πn}{3}, x = \frac{7 π}{12} + \frac{2 πn}{3}

0 = cos (θ)

sec^{2} (x) + 3 tan (x) = 5

2 sin (θ) + 1 = csc (θ)

cot (x) - 1 = csc (x)

- 6 cos^{2} (θ) - 3 cos (θ) + 1 = - 4 cos (θ)

What is the general solution for 2sin(3x)+sqrt(2)=0 ?
The general solution for 2sin(3x)+sqrt(2)=0 is x=(5pi}{12}+(2pin)/3 ,x=(7pi)/(12)+\frac{2pin)/3