What is the general solution for 0=5*sin(2pi*(-0.25-x)) ?

The general solution for 0=5*sin(2pi*(-0.25-x)) is x=-n-0.25,x=-n-0.75

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0=5sin(2pi(-0.25-x))

Solution

0 = 5 \cdot sin (2 π \cdot (- 0.25 - x))

Solution

x = - n - 0.25, x = - n - 0.75

Degrees

x = - 14.32394 \dots^{\circ} - 57.29577 \dots^{\circ} n, x = - 42.97183 \dots^{\circ} - 57.29577 \dots^{\circ} n

Solution steps

0 = 5 sin (2 π (- 0.25 - x))

Switch sides

5 sin (2 π (- 0.25 - x)) = 0

Divide both sides by

5

5 sin (2 π (- 0.25 - x)) = 0

Divide both sides by

5

\frac{5 sin ( 2 π ( - 0.25 - x ) )}{5} = \frac{0}{5}

Simplify

sin (2 π (- 0.25 - x)) = 0

sin (2 π (- 0.25 - x)) = 0

General solutions for

sin (2 π (- 0.25 - 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 (- 0.25 - x) = 0 + 2 πn, 2 π (- 0.25 - x) = π + 2 πn

2 π (- 0.25 - x) = 0 + 2 πn, 2 π (- 0.25 - x) = π + 2 πn

Solve

2 π (- 0.25 - x) = 0 + 2 πn : x = - n - 0.25

2 π (- 0.25 - x) = 0 + 2 πn

0 + 2 πn = 2 πn

2 π (- 0.25 - x) = 2 πn

Divide both sides by

2 π

2 π (- 0.25 - x) = 2 πn

Divide both sides by

2 π

\frac{2 π ( - 0.25 - x )}{2 π} = \frac{2 πn}{2 π}

Simplify

\frac{2 π ( - 0.25 - x )}{2 π} = \frac{2 πn}{2 π}

Simplify

\frac{2 π ( - 0.25 - x )}{2 π} : - 0.25 - x

\frac{2 π ( - 0.25 - x )}{2 π}

Divide the numbers:

\frac{2}{2} = 1

= \frac{π ( - x - 0.25 )}{π}

Cancel the common factor:

π

= - 0.25 - 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

- 0.25 - x = n

- 0.25 - x = n

- 0.25 - x = n

Move

0.25

to the right side

- 0.25 - x = n

Add

0.25

to both sides

- 0.25 - x + 0.25 = n + 0.25

Simplify

- x = n + 0.25

- x = n + 0.25

Divide both sides by

- 1

- x = n + 0.25

Divide both sides by

- 1

\frac{- x}{- 1} = \frac{n}{- 1} + \frac{0.25}{- 1}

Simplify

\frac{- x}{- 1} = \frac{n}{- 1} + \frac{0.25}{- 1}

Simplify

\frac{- x}{- 1} : x

\frac{- x}{- 1}

Apply the fraction rule:

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

= \frac{x}{1}

Apply rule

\frac{a}{1} = a

= x

Simplify

\frac{n}{- 1} + \frac{0.25}{- 1} : - n - 0.25

\frac{n}{- 1} + \frac{0.25}{- 1}

\frac{n}{- 1} = - n

\frac{n}{- 1}

Apply the fraction rule:

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

= - \frac{n}{1}

Apply rule

\frac{a}{1} = a

= - n

= - n + \frac{0.25}{- 1}

\frac{0.25}{- 1} = - 0.25

\frac{0.25}{- 1}

Apply the fraction rule:

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

= - \frac{0.25}{1}

Apply rule

\frac{a}{1} = a

= - 0.25

= - n - 0.25

x = - n - 0.25

x = - n - 0.25

x = - n - 0.25

Solve

2 π (- 0.25 - x) = π + 2 πn : x = - n - 0.75

2 π (- 0.25 - x) = π + 2 πn

Divide both sides by

2 π

2 π (- 0.25 - x) = π + 2 πn

Divide both sides by

2 π

\frac{2 π ( - 0.25 - x )}{2 π} = \frac{π}{2 π} + \frac{2 πn}{2 π}

Simplify

\frac{2 π ( - 0.25 - x )}{2 π} = \frac{π}{2 π} + \frac{2 πn}{2 π}

Simplify

\frac{2 π ( - 0.25 - x )}{2 π} : - 0.25 - x

\frac{2 π ( - 0.25 - x )}{2 π}

Divide the numbers:

\frac{2}{2} = 1

= \frac{π ( - x - 0.25 )}{π}

Cancel the common factor:

π

= - 0.25 - 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

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

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

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

Move

0.25

to the right side

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

Add

0.25

to both sides

- 0.25 - x + 0.25 = \frac{1}{2} + n + 0.25

Simplify

- 0.25 - x + 0.25 = \frac{1}{2} + n + 0.25

Simplify

- 0.25 - x + 0.25 : - x

- 0.25 - x + 0.25

Add similar elements:

- 0.25 + 0.25 = 0

= - x

Simplify

\frac{1}{2} + n + 0.25 : n + 0.75

\frac{1}{2} + n + 0.25

Convert element to a decimal form

\frac{1}{2} = 0.5

= 0.5 + n + 0.25

Add the numbers:

0.5 + 0.25 = 0.75

= n + 0.75

- x = n + 0.75

- x = n + 0.75

- x = n + 0.75

Divide both sides by

- 1

- x = n + 0.75

Divide both sides by

- 1

\frac{- x}{- 1} = \frac{n}{- 1} + \frac{0.75}{- 1}

Simplify

\frac{- x}{- 1} = \frac{n}{- 1} + \frac{0.75}{- 1}

Simplify

\frac{- x}{- 1} : x

\frac{- x}{- 1}

Apply the fraction rule:

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

= \frac{x}{1}

Apply rule

\frac{a}{1} = a

= x

Simplify

\frac{n}{- 1} + \frac{0.75}{- 1} : - n - 0.75

\frac{n}{- 1} + \frac{0.75}{- 1}

\frac{n}{- 1} = - n

\frac{n}{- 1}

Apply the fraction rule:

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

= - \frac{n}{1}

Apply rule

\frac{a}{1} = a

= - n

= - n + \frac{0.75}{- 1}

\frac{0.75}{- 1} = - 0.75

\frac{0.75}{- 1}

Apply the fraction rule:

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

= - \frac{0.75}{1}

Apply rule

\frac{a}{1} = a

= - 0.75

= - n - 0.75

x = - n - 0.75

x = - n - 0.75

x = - n - 0.75

x = - n - 0.25, x = - n - 0.75

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Frequently Asked Questions (FAQ)

What is the general solution for 0=5*sin(2pi*(-0.25-x)) ?
The general solution for 0=5*sin(2pi*(-0.25-x)) is x=-n-0.25,x=-n-0.75