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

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

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Popular >

sin(sqrt(2)x)=0

Solution

sin (2 x) = 0

Solution

x = 2 πn, x = \frac{π}{2} + 2 πn

Degrees

x = 0^{\circ} + 254.55844 \dots^{\circ} n, x = 127.27922 \dots^{\circ} + 254.55844 \dots^{\circ} n

Solution steps

sin (2 x) = 0

General solutions for

sin (2 x) = 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}

2 x = 0 + 2 πn, 2 x = π + 2 πn

2 x = 0 + 2 πn, 2 x = π + 2 πn

Solve

2 x = 0 + 2 πn : x = 2 πn

2 x = 0 + 2 πn

0 + 2 πn = 2 πn

2 x = 2 πn

Divide both sides by

2

2 x = 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{2 πn}{2}

Simplify

\frac{2 x}{2} = \frac{2 πn}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Cancel the common factor:

2

= x

Simplify

\frac{2 πn}{2} : 2 πn

\frac{2 πn}{2}

Apply radical rule:

n a = a^{\frac{1}{n}}

2 = 2^{\frac{1}{2}}

= \frac{2 πn}{2 ^{\frac{1}{2}}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{2 ^{1}}{2 ^{\frac{1}{2}}} = 2^{1 - \frac{1}{2}}

= 2^{- \frac{1}{2} + 1} πn

Subtract the numbers:

1 - \frac{1}{2} = \frac{1}{2}

= 2^{\frac{1}{2}} πn

Apply radical rule:

a^{\frac{1}{n}} = n a

2^{\frac{1}{2}} = 2

= 2 πn

x = 2 πn

x = 2 πn

x = 2 πn

Solve

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

2 x = π + 2 πn

Divide both sides by

2

2 x = π + 2 πn

Divide both sides by

2

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

Simplify

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

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Cancel the common factor:

2

= x

Simplify

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

\frac{π}{2} + \frac{2 πn}{2}

Cancel

\frac{2 πn}{2} : 2 πn

\frac{2 πn}{2}

Cancel

\frac{2 πn}{2} : 2 πn

\frac{2 πn}{2}

Apply radical rule:

n a = a^{\frac{1}{n}}

2 = 2^{\frac{1}{2}}

= \frac{2 πn}{2 ^{\frac{1}{2}}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{2 ^{1}}{2 ^{\frac{1}{2}}} = 2^{1 - \frac{1}{2}}

= 2^{- \frac{1}{2} + 1} πn

Subtract the numbers:

1 - \frac{1}{2} = \frac{1}{2}

= 2^{\frac{1}{2}} πn

Apply radical rule:

a^{\frac{1}{n}} = n a

2^{\frac{1}{2}} = 2

= 2 πn

= 2 πn

= \frac{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

x = 2 πn, x = \frac{π}{2} + 2 πn

Graph

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Frequently Asked Questions (FAQ)

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