What is the general solution for 0=4sin(4x+3pi) ?

The general solution for 0=4sin(4x+3pi) is x=(pin)/2-(3pi)/4 ,x=-pi/2+(pin)/2

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0=4sin(4x+3pi)

Solution

0 = 4 sin (4 x + 3 π)

Solution

x = \frac{πn}{2} - \frac{3 π}{4}, x = - \frac{π}{2} + \frac{πn}{2}

Degrees

x = - 13 5^{\circ} + 9 0^{\circ} n, x = - 9 0^{\circ} + 9 0^{\circ} n

Solution steps

0 = 4 sin (4 x + 3 π)

Switch sides

4 sin (4 x + 3 π) = 0

Divide both sides by

4

4 sin (4 x + 3 π) = 0

Divide both sides by

4

\frac{4 sin ( 4 x + 3 π )}{4} = \frac{0}{4}

Simplify

sin (4 x + 3 π) = 0

sin (4 x + 3 π) = 0

General solutions for

sin (4 x + 3 π) = 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}

4 x + 3 π = 0 + 2 πn, 4 x + 3 π = π + 2 πn

4 x + 3 π = 0 + 2 πn, 4 x + 3 π = π + 2 πn

Solve

4 x + 3 π = 0 + 2 πn : x = \frac{πn}{2} - \frac{3 π}{4}

4 x + 3 π = 0 + 2 πn

0 + 2 πn = 2 πn

4 x + 3 π = 2 πn

Move

3 π

to the right side

4 x + 3 π = 2 πn

Subtract

3 π

from both sides

4 x + 3 π - 3 π = 2 πn - 3 π

Simplify

4 x = 2 πn - 3 π

4 x = 2 πn - 3 π

Divide both sides by

4

4 x = 2 πn - 3 π

Divide both sides by

4

\frac{4 x}{4} = \frac{2 πn}{4} - \frac{3 π}{4}

Simplify

x = \frac{πn}{2} - \frac{3 π}{4}

x = \frac{πn}{2} - \frac{3 π}{4}

Solve

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

4 x + 3 π = π + 2 πn

Move

3 π

to the right side

4 x + 3 π = π + 2 πn

Subtract

3 π

from both sides

4 x + 3 π - 3 π = π + 2 πn - 3 π

Simplify

4 x = - 2 π + 2 πn

4 x = - 2 π + 2 πn

Divide both sides by

4

4 x = - 2 π + 2 πn

Divide both sides by

4

\frac{4 x}{4} = - \frac{2 π}{4} + \frac{2 πn}{4}

Simplify

\frac{4 x}{4} = - \frac{2 π}{4} + \frac{2 πn}{4}

Simplify

\frac{4 x}{4} : x

\frac{4 x}{4}

Divide the numbers:

\frac{4}{4} = 1

= x

Simplify

- \frac{2 π}{4} + \frac{2 πn}{4} : - \frac{π}{2} + \frac{πn}{2}

- \frac{2 π}{4} + \frac{2 πn}{4}

Cancel

\frac{2 π}{4} : \frac{π}{2}

\frac{2 π}{4}

Cancel the common factor:

2

= \frac{π}{2}

= - \frac{π}{2} + \frac{2 πn}{4}

Cancel

\frac{2 πn}{4} : \frac{πn}{2}

\frac{2 πn}{4}

Cancel the common factor:

2

= \frac{πn}{2}

= - \frac{π}{2} + \frac{πn}{2}

x = - \frac{π}{2} + \frac{πn}{2}

x = - \frac{π}{2} + \frac{πn}{2}

x = - \frac{π}{2} + \frac{πn}{2}

x = \frac{πn}{2} - \frac{3 π}{4}, x = - \frac{π}{2} + \frac{πn}{2}

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Frequently Asked Questions (FAQ)

What is the general solution for 0=4sin(4x+3pi) ?
The general solution for 0=4sin(4x+3pi) is x=(pin)/2-(3pi)/4 ,x=-pi/2+(pin)/2