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

The general solution for sin(2pix)=0 is x=n,x= 1/2+n

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sin(2pix)=0

Solution

sin (2 π x) = 0

Solution

x = n, x = \frac{1}{2} + n

Degrees

x = 0^{\circ}, x = 28.64788 \dots^{\circ}

Solution steps

sin (2 π x) = 0

General solutions for

sin (2 π 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 π x = 0 + 2 πn, 2 π x = π + 2 πn

2 π x = 0 + 2 πn, 2 π x = π + 2 πn

Solve

2 π x = 0 + 2 πn : x = n

2 π x = 0 + 2 πn

0 + 2 πn = 2 πn

2 π x = 2 πn

Divide both sides by

2 π

2 π x = 2 πn

Divide both sides by

2 π

\frac{2 π x}{2 π} = \frac{2 πn}{2 π}

Simplify

\frac{2 π x}{2 π} = \frac{2 πn}{2 π}

Simplify

\frac{2 π x}{2 π} : x

\frac{2 π x}{2 π}

Divide the numbers:

\frac{2}{2} = 1

= \frac{π x}{π}

Cancel the common factor:

π

= x

Simplify

\frac{2 πn}{2 π} : n

\frac{2 πn}{2 π}

Divide the numbers:

\frac{2}{2} = 1

= \frac{πn}{π}

Cancel the common factor:

π

= n

x = n

x = n

x = n

Solve

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

2 π x = π + 2 πn

Divide both sides by

2 π

2 π x = π + 2 πn

Divide both sides by

2 π

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

Simplify

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

Simplify

\frac{2 π x}{2 π} : x

\frac{2 π x}{2 π}

Divide the numbers:

\frac{2}{2} = 1

= \frac{π x}{π}

Cancel the common factor:

π

= x

Simplify

\frac{π}{2 π} + \frac{2 πn}{2 π} : \frac{1}{2} + n

\frac{π}{2 π} + \frac{2 πn}{2 π}

Cancel

\frac{π}{2 π} : \frac{1}{2}

\frac{π}{2 π}

Cancel the common factor:

π

= \frac{1}{2}

= \frac{1}{2} + \frac{2 πn}{2 π}

Cancel

\frac{2 πn}{2 π} : n

\frac{2 πn}{2 π}

Cancel

\frac{2 πn}{2 π} : n

\frac{2 πn}{2 π}

Divide the numbers:

\frac{2}{2} = 1

= \frac{πn}{π}

Cancel the common factor:

π

= n

= n

= \frac{1}{2} + n

x = \frac{1}{2} + n

x = \frac{1}{2} + n

x = \frac{1}{2} + n

x = n, x = \frac{1}{2} + n

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tan (θ) = 2.2

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0 = 1 + 2 cos (x)

tan(x)=0.81

tan (x) = 0.81

Frequently Asked Questions (FAQ)

What is the general solution for sin(2pix)=0 ?
The general solution for sin(2pix)=0 is x=n,x= 1/2+n