What is the general solution for 2sin(3x+1)+1=1 ?

The general solution for 2sin(3x+1)+1=1 is x=(2pin)/3-1/3 ,x= pi/3+(2pin)/3-1/3

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

Solution

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

Solution

x = \frac{2 πn}{3} - \frac{1}{3}, x = \frac{π}{3} + \frac{2 πn}{3} - \frac{1}{3}

Degrees

x = - 19.09859 \dots^{\circ} + 12 0^{\circ} n, x = 40.90140 \dots^{\circ} + 12 0^{\circ} n

Solution steps

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

Subtract

1

from both sides

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

Simplify

2 sin (3 x + 1) = 0

Divide both sides by

2

2 sin (3 x + 1) = 0

Divide both sides by

2

\frac{2 sin ( 3 x + 1 )}{2} = \frac{0}{2}

Simplify

sin (3 x + 1) = 0

sin (3 x + 1) = 0

General solutions for

sin (3 x + 1) = 0

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 + 1 = 0 + 2 πn, 3 x + 1 = π + 2 πn

3 x + 1 = 0 + 2 πn, 3 x + 1 = π + 2 πn

Solve

3 x + 1 = 0 + 2 πn : x = \frac{2 πn}{3} - \frac{1}{3}

3 x + 1 = 0 + 2 πn

0 + 2 πn = 2 πn

3 x + 1 = 2 πn

Move

1

to the right side

3 x + 1 = 2 πn

Subtract

1

from both sides

3 x + 1 - 1 = 2 πn - 1

Simplify

3 x = 2 πn - 1

3 x = 2 πn - 1

Divide both sides by

3

3 x = 2 πn - 1

Divide both sides by

3

\frac{3 x}{3} = \frac{2 πn}{3} - \frac{1}{3}

Simplify

x = \frac{2 πn}{3} - \frac{1}{3}

x = \frac{2 πn}{3} - \frac{1}{3}

Solve

3 x + 1 = π + 2 πn : x = \frac{π}{3} + \frac{2 πn}{3} - \frac{1}{3}

3 x + 1 = π + 2 πn

Move

1

to the right side

3 x + 1 = π + 2 πn

Subtract

1

from both sides

3 x + 1 - 1 = π + 2 πn - 1

Simplify

3 x = π + 2 πn - 1

3 x = π + 2 πn - 1

Divide both sides by

3

3 x = π + 2 πn - 1

Divide both sides by

3

\frac{3 x}{3} = \frac{π}{3} + \frac{2 πn}{3} - \frac{1}{3}

Simplify

x = \frac{π}{3} + \frac{2 πn}{3} - \frac{1}{3}

x = \frac{π}{3} + \frac{2 πn}{3} - \frac{1}{3}

x = \frac{2 πn}{3} - \frac{1}{3}, x = \frac{π}{3} + \frac{2 πn}{3} - \frac{1}{3}

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Frequently Asked Questions (FAQ)

What is the general solution for 2sin(3x+1)+1=1 ?
The general solution for 2sin(3x+1)+1=1 is x=(2pin)/3-1/3 ,x= pi/3+(2pin)/3-1/3