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

The general solution for -2sin(x)-1=0 is x=(7pi)/6+2pin,x=(11pi)/6+2pin

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-2sin(x)-1=0

- 2 sin (x) - 1 = 0

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

Degrees

x = 21 0^{\circ} + 36 0^{\circ} n, x = 33 0^{\circ} + 36 0^{\circ} n

Solution steps

- 2 sin (x) - 1 = 0

Move

1

to the right side

- 2 sin (x) - 1 = 0

Add

1

to both sides

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

Simplify

- 2 sin (x) = 1

- 2 sin (x) = 1

Divide both sides by

- 2

- 2 sin (x) = 1

Divide both sides by

- 2

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

Simplify

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

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

General solutions for

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

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

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

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

3 sin (θ) + cos (θ) = 1

3 csc (x) + 2 = 0

2 cos^{2} (x) = sin (x) - 1

tan (2 x) = 5 sin (2 x)

2 sin^{2} (x) - 7 sin (x) - 4 = 0

What is the general solution for -2sin(x)-1=0 ?
The general solution for -2sin(x)-1=0 is x=(7pi)/6+2pin,x=(11pi)/6+2pin