en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2sin(3x+pi)=-1

Solution

2 sin (3 x + π) = - 1

Solution

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

+1

Degrees

x = 1 0^{\circ} + 12 0^{\circ} n, x = 5 0^{\circ} + 12 0^{\circ} n

Solution steps

2 sin (3 x + π) = - 1

Divide both sides by

2

2 sin (3 x + π) = - 1

Divide both sides by

2

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

Simplify

sin (3 x + π) = - \frac{1}{2}

sin (3 x + π) = - \frac{1}{2}

General solutions for

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

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

Solve

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

3 x + π = \frac{7 π}{6} + 2 πn

Move

π

to the right side

3 x + π = \frac{7 π}{6} + 2 πn

Subtract

π

from both sides

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

Simplify

3 x = \frac{7 π}{6} + 2 πn - π

3 x = \frac{7 π}{6} + 2 πn - π

Divide both sides by

3

3 x = \frac{7 π}{6} + 2 πn - π

Divide both sides by

3

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

Simplify

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

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

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

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

Group like terms

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

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

\frac{\frac{7 π}{6}}{3}

Apply the fraction rule:

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

= \frac{7 π}{6 \cdot 3}

Multiply the numbers:

6 \cdot 3 = 18

= \frac{7 π}{18}

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

Group like terms

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

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

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

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

Solve

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

3 x + π = \frac{11 π}{6} + 2 πn

Move

π

to the right side

3 x + π = \frac{11 π}{6} + 2 πn

Subtract

π

from both sides

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

Simplify

3 x = \frac{11 π}{6} + 2 πn - π

3 x = \frac{11 π}{6} + 2 πn - π

Divide both sides by

3

3 x = \frac{11 π}{6} + 2 πn - π

Divide both sides by

3

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

Simplify

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

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

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

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

Group like terms

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

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

\frac{\frac{11 π}{6}}{3}

Apply the fraction rule:

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

= \frac{11 π}{6 \cdot 3}

Multiply the numbers:

6 \cdot 3 = 18

= \frac{11 π}{18}

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

Group like terms

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

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

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

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

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

Popular Examples

solvefor t,f=cos(at)solve for

t, f = cos (a t)

sqrt(2)cos(x)+1=0,pi<x<4pi

2 cos (x) + 1 = 0, π < x < 4 π

cos (3 x) = 3

4cos^2(θ)-5cos(θ)=-4cos(θ)+3

4 cos^{2} (θ) - 5 cos (θ) = - 4 cos (θ) + 3

solvefor x,cos(x)=-0.5 solve for

x, cos (x) = - 0.5