What is the general solution for -2sin(-3x)-1=0 ?

The general solution for -2sin(-3x)-1=0 is x=-(7pi}{18}-(2pin)/3 ,x=-(11pi)/(18)-\frac{2pin)/3

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-2sin(-3x)-1=0

- 2 sin (- 3 x) - 1 = 0

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

Solution steps

- 2 sin (- 3 x) - 1 = 0

Move

1

to the right side

- 2 sin (- 3 x) = 1

Divide both sides by

- 2

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}

tan (x) + sin (x) tan (x) = 0, - π \leq x < π

4 sin^{2} (x) - sin (x) - 2 = 0

2 cos (x) sin (x) + 1 cos (x) = 0

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

3 sin (x) = - 2

What is the general solution for -2sin(-3x)-1=0 ?
The general solution for -2sin(-3x)-1=0 is x=-(7pi}{18}-(2pin)/3 ,x=-(11pi)/(18)-\frac{2pin)/3