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

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

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2sin(x-1)+1=0

Solution

2 sin (x - 1) + 1 = 0

Solution

x = \frac{7 π}{6} + 2 πn + 1, x = \frac{11 π}{6} + 2 πn + 1

Degrees

x = 267.29577 \dots^{\circ} + 36 0^{\circ} n, x = 387.29577 \dots^{\circ} + 36 0^{\circ} n

Solution steps

2 sin (x - 1) + 1 = 0

Move

1

to the right side

2 sin (x - 1) + 1 = 0

Subtract

1

from both sides

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

Simplify

2 sin (x - 1) = - 1

2 sin (x - 1) = - 1

Divide both sides by

2

2 sin (x - 1) = - 1

Divide both sides by

2

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

Simplify

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

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

General solutions for

sin (x - 1) = - \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 - 1 = \frac{7 π}{6} + 2 πn, x - 1 = \frac{11 π}{6} + 2 πn

x - 1 = \frac{7 π}{6} + 2 πn, x - 1 = \frac{11 π}{6} + 2 πn

Solve

x - 1 = \frac{7 π}{6} + 2 πn : x = \frac{7 π}{6} + 2 πn + 1

x - 1 = \frac{7 π}{6} + 2 πn

Move

1

to the right side

x - 1 = \frac{7 π}{6} + 2 πn

Add

1

to both sides

x - 1 + 1 = \frac{7 π}{6} + 2 πn + 1

Simplify

x = \frac{7 π}{6} + 2 πn + 1

x = \frac{7 π}{6} + 2 πn + 1

Solve

x - 1 = \frac{11 π}{6} + 2 πn : x = \frac{11 π}{6} + 2 πn + 1

x - 1 = \frac{11 π}{6} + 2 πn

Move

1

to the right side

x - 1 = \frac{11 π}{6} + 2 πn

Add

1

to both sides

x - 1 + 1 = \frac{11 π}{6} + 2 πn + 1

Simplify

x = \frac{11 π}{6} + 2 πn + 1

x = \frac{11 π}{6} + 2 πn + 1

x = \frac{7 π}{6} + 2 πn + 1, x = \frac{11 π}{6} + 2 πn + 1

Popular Examples

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csc(x)+2=0,0<= x<= 2pi

csc (x) + 2 = 0, 0 \leq x \leq 2 π

tan(x)=3.7

tan (x) = 3.7

0=12cos(pi/3 t)+8

0 = 12 cos (\frac{π}{3} t) + 8

5=20.39sin(θ)cos(θ)

5 = 20.39 sin (θ) cos (θ)

Frequently Asked Questions (FAQ)

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