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

Solution

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

Solution

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

Degrees

x = - 7 0^{\circ} - 12 0^{\circ} n, x = - 11 0^{\circ} - 12 0^{\circ} n

Solution steps

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

Move

1

to the right side

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

Add

1

to both sides

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

Simplify

- 2 sin (- 3 x) = 1

- 2 sin (- 3 x) = 1

Divide both sides by

- 2

- 2 sin (- 3 x) = 1

Divide both sides by

- 2

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

Simplify

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

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

General solutions for

sin (- 3 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}

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

- 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}

- 3 x = \frac{7 π}{6} + 2 πn

Divide both sides by

- 3

- 3 x = \frac{7 π}{6} + 2 πn

Divide both sides by

- 3

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

Simplify

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

Simplify

\frac{- 3 x}{- 3} : x

\frac{- 3 x}{- 3}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

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

\frac{\frac{7 π}{6}}{- 3} + \frac{2 πn}{- 3}

\frac{\frac{7 π}{6}}{- 3} = - \frac{7 π}{18}

\frac{\frac{7 π}{6}}{- 3}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{\frac{7 π}{6}}{3}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

\frac{\frac{7 π}{6}}{3} = \frac{7 π}{6 \cdot 3}

= - \frac{7 π}{6 \cdot 3}

Multiply the numbers:

6 \cdot 3 = 18

= - \frac{7 π}{18}

= - \frac{7 π}{18} + \frac{2 πn}{- 3}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{7 π}{18} - \frac{2 πn}{3}

x = - \frac{7 π}{18} - \frac{2 πn}{3}

x = - \frac{7 π}{18} - \frac{2 πn}{3}

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}

- 3 x = \frac{11 π}{6} + 2 πn

Divide both sides by

- 3

- 3 x = \frac{11 π}{6} + 2 πn

Divide both sides by

- 3

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

Simplify

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

Simplify

\frac{- 3 x}{- 3} : x

\frac{- 3 x}{- 3}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

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

\frac{\frac{11 π}{6}}{- 3} + \frac{2 πn}{- 3}

\frac{\frac{11 π}{6}}{- 3} = - \frac{11 π}{18}

\frac{\frac{11 π}{6}}{- 3}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{\frac{11 π}{6}}{3}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

\frac{\frac{11 π}{6}}{3} = \frac{11 π}{6 \cdot 3}

= - \frac{11 π}{6 \cdot 3}

Multiply the numbers:

6 \cdot 3 = 18

= - \frac{11 π}{18}

= - \frac{11 π}{18} + \frac{2 πn}{- 3}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{11 π}{18} - \frac{2 πn}{3}

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

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

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}

Graph

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Frequently Asked Questions (FAQ)

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