What is the general solution for sin(4(x-pi/4))=0 ?

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

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sin(4(x-pi/4))=0

Solution

sin (4 (x - \frac{π}{4})) = 0

Solution

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

Degrees

x = 4 5^{\circ} + 9 0^{\circ} n, x = 9 0^{\circ} + 9 0^{\circ} n

Solution steps

sin (4 (x - \frac{π}{4})) = 0

General solutions for

sin (4 (x - \frac{π}{4})) = 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 - \frac{π}{4}) = 0 + 2 πn, 4 (x - \frac{π}{4}) = π + 2 πn

4 (x - \frac{π}{4}) = 0 + 2 πn, 4 (x - \frac{π}{4}) = π + 2 πn

Solve

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

4 (x - \frac{π}{4}) = 0 + 2 πn

0 + 2 πn = 2 πn

4 (x - \frac{π}{4}) = 2 πn

Divide both sides by

4

4 (x - \frac{π}{4}) = 2 πn

Divide both sides by

4

\frac{4 ( x - \frac{π}{4} )}{4} = \frac{2 πn}{4}

Simplify

x - \frac{π}{4} = \frac{πn}{2}

x - \frac{π}{4} = \frac{πn}{2}

Move

\frac{π}{4}

to the right side

x - \frac{π}{4} = \frac{πn}{2}

Add

\frac{π}{4}

to both sides

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

Simplify

x = \frac{πn}{2} + \frac{π}{4}

x = \frac{πn}{2} + \frac{π}{4}

Solve

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

4 (x - \frac{π}{4}) = π + 2 πn

Divide both sides by

4

4 (x - \frac{π}{4}) = π + 2 πn

Divide both sides by

4

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

Simplify

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

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

Move

\frac{π}{4}

to the right side

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

Add

\frac{π}{4}

to both sides

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

Simplify

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

Simplify

x - \frac{π}{4} + \frac{π}{4} : x

x - \frac{π}{4} + \frac{π}{4}

Add similar elements:

- \frac{π}{4} + \frac{π}{4} = 0

= x

Simplify

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

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

Group like terms

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

Combine the fractions

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

Apply rule

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

= \frac{π + π}{4}

Add similar elements:

π + π = 2 π

= \frac{2 π}{4}

Cancel the common factor:

2

= \frac{π}{2}

= \frac{π}{2} + \frac{πn}{2}

Since the denominators are equal, combine the fractions:

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

= \frac{π + πn}{2}

x = \frac{π + πn}{2}

x = \frac{π + πn}{2}

x = \frac{π + πn}{2}

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

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Frequently Asked Questions (FAQ)

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