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

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

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3+6sin(3t)=0

3 + 6 sin (3 t) = 0

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

Solution steps

3 + 6 sin (3 t) = 0

Move

3

to the right side

6 sin (3 t) = - 3

Divide both sides by

6

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

General solutions for

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

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

Solve

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

Solve

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

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

cos (2 θ) = 11 sin (θ) - 5

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

x, sec (x) = - 3.5

4 tan (θ) = 3 + tan (θ)

tan (2 x) + sec (2 x) = 10

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