What is the general solution for 3+6sin(3x)=0 ?

The general solution for 3+6sin(3x)=0 is x=(7pi}{18}+(2pin)/3 ,x=(11pi)/(18)+\frac{2pin)/3

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3+6sin(3x)=0

3 + 6 sin (3 x) = 0

x = \frac{7 π}{18} + \frac{2 πn}{3}, x = \frac{11 π}{18} + \frac{2 πn}{3}

Solution steps

3 + 6 sin (3 x) = 0

Move

3

to the right side

6 sin (3 x) = - 3

Divide both sides by

6

sin (3 x) = - \frac{1}{2}

General solutions for

sin (3 x) = - \frac{1}{2}

3 x = \frac{7 π}{6} + 2 πn, 3 x = \frac{11 π}{6} + 2 πn

Solve

3 x = \frac{7 π}{6} + 2 πn : x = \frac{7 π}{18} + \frac{2 πn}{3}

Solve

3 x = \frac{11 π}{6} + 2 πn : x = \frac{11 π}{18} + \frac{2 πn}{3}

x = \frac{7 π}{18} + \frac{2 πn}{3}, x = \frac{11 π}{18} + \frac{2 πn}{3}

cos (x) cos (2 x) - sin (x) sin (2 x) = 0

θ, x = 5 tan (θ)

cos (x) tan (x) cos (x) = 0, 0 \leq x \leq 2 π

3 sin (x) + 5 cos (x) + 5 = 0

2 cot (x) = 2

What is the general solution for 3+6sin(3x)=0 ?
The general solution for 3+6sin(3x)=0 is x=(7pi}{18}+(2pin)/3 ,x=(11pi)/(18)+\frac{2pin)/3