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

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

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Popular >

0=2sin(x+1)+1

Solution

0 = 2 sin (x + 1) + 1

Solution

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

Degrees

x = 152.70422 \dots^{\circ} + 36 0^{\circ} n, x = 272.70422 \dots^{\circ} + 36 0^{\circ} n

Solution steps

0 = 2 sin (x + 1) + 1

Switch sides

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

Subtract

1

from 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

Subtract

1

from 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

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Frequently Asked Questions (FAQ)

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