What is the general solution for sin((pix)/2)=0 ?

The general solution for sin((pix)/2)=0 is x=4n,x=2+4n

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sin((pix)/2)=0

Solution

sin (\frac{π x}{2}) = 0

Solution

x = 4 n, x = 2 + 4 n

Degrees

x = 0^{\circ} + 229.18311 \dots^{\circ} n, x = 114.59155 \dots^{\circ} + 229.18311 \dots^{\circ} n

Solution steps

sin (\frac{π x}{2}) = 0

General solutions for

sin (\frac{π x}{2}) = 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}

\frac{π x}{2} = 0 + 2 πn, \frac{π x}{2} = π + 2 πn

\frac{π x}{2} = 0 + 2 πn, \frac{π x}{2} = π + 2 πn

Solve

\frac{π x}{2} = 0 + 2 πn : x = 4 n

\frac{π x}{2} = 0 + 2 πn

0 + 2 πn = 2 πn

\frac{π x}{2} = 2 πn

Multiply both sides by

2

\frac{π x}{2} = 2 πn

Multiply both sides by

2

\frac{2 π x}{2} = 2 \cdot 2 πn

Simplify

π x = 4 πn

π x = 4 πn

Divide both sides by

π

π x = 4 πn

Divide both sides by

π

\frac{π x}{π} = \frac{4 πn}{π}

Simplify

x = 4 n

x = 4 n

Solve

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

\frac{π x}{2} = π + 2 πn

Multiply both sides by

2

\frac{π x}{2} = π + 2 πn

Multiply both sides by

2

\frac{2 π x}{2} = 2 π + 2 \cdot 2 πn

Simplify

π x = 2 π + 4 πn

π x = 2 π + 4 πn

Divide both sides by

π

π x = 2 π + 4 πn

Divide both sides by

π

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

Simplify

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

Simplify

\frac{π x}{π} : x

\frac{π x}{π}

Cancel the common factor:

π

= x

Simplify

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

\frac{2 π}{π} + \frac{4 πn}{π}

Cancel

\frac{2 π}{π} : 2

\frac{2 π}{π}

Cancel the common factor:

π

= 2

= 2 + \frac{4 πn}{π}

Cancel

\frac{4 πn}{π} : 4 n

\frac{4 πn}{π}

Cancel the common factor:

π

= 4 n

= 2 + 4 n

x = 2 + 4 n

x = 2 + 4 n

x = 2 + 4 n

x = 4 n, x = 2 + 4 n

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Frequently Asked Questions (FAQ)

What is the general solution for sin((pix)/2)=0 ?
The general solution for sin((pix)/2)=0 is x=4n,x=2+4n