What is the general solution for 2=-8*sin(4x) ?

The general solution for 2=-8*sin(4x) is x=-(0.25268…)/4+(pin)/2 ,x= pi/4+(0.25268…)/4+(pin)/2

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2=-8*sin(4x)

Solution

2 = - 8 \cdot sin (4 x)

Solution

x = - \frac{0.25268 \dots}{4} + \frac{πn}{2}, x = \frac{π}{4} + \frac{0.25268 \dots}{4} + \frac{πn}{2}

Degrees

x = - 3.61937 \dots^{\circ} + 9 0^{\circ} n, x = 48.61937 \dots^{\circ} + 9 0^{\circ} n

Solution steps

2 = - 8 sin (4 x)

Switch sides

- 8 sin (4 x) = 2

Divide both sides by

- 8

- 8 sin (4 x) = 2

Divide both sides by

- 8

\frac{- 8 sin ( 4 x )}{- 8} = \frac{2}{- 8}

Simplify

\frac{- 8 sin ( 4 x )}{- 8} = \frac{2}{- 8}

Simplify

\frac{- 8 sin ( 4 x )}{- 8} : sin (4 x)

\frac{- 8 sin ( 4 x )}{- 8}

Apply the fraction rule:

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

= \frac{8 sin ( 4 x )}{8}

Divide the numbers:

\frac{8}{8} = 1

= sin (4 x)

Simplify

\frac{2}{- 8} : - \frac{1}{4}

\frac{2}{- 8}

Apply the fraction rule:

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

= - \frac{2}{8}

Cancel the common factor:

2

= - \frac{1}{4}

sin (4 x) = - \frac{1}{4}

sin (4 x) = - \frac{1}{4}

sin (4 x) = - \frac{1}{4}

Apply trig inverse properties

sin (4 x) = - \frac{1}{4}

General solutions for

sin (4 x) = - \frac{1}{4}

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

4 x = arcsin (- \frac{1}{4}) + 2 πn, 4 x = π + arcsin (\frac{1}{4}) + 2 πn

4 x = arcsin (- \frac{1}{4}) + 2 πn, 4 x = π + arcsin (\frac{1}{4}) + 2 πn

Solve

4 x = arcsin (- \frac{1}{4}) + 2 πn : x = - \frac{arcsin ( \frac{1}{4} )}{4} + \frac{πn}{2}

4 x = arcsin (- \frac{1}{4}) + 2 πn

Simplify

arcsin (- \frac{1}{4}) + 2 πn : - arcsin (\frac{1}{4}) + 2 πn

arcsin (- \frac{1}{4}) + 2 πn

Use the following property:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{1}{4}) = - arcsin (\frac{1}{4})

= - arcsin (\frac{1}{4}) + 2 πn

4 x = - arcsin (\frac{1}{4}) + 2 πn

Divide both sides by

4

4 x = - arcsin (\frac{1}{4}) + 2 πn

Divide both sides by

4

\frac{4 x}{4} = - \frac{arcsin ( \frac{1}{4} )}{4} + \frac{2 πn}{4}

Simplify

x = - \frac{arcsin ( \frac{1}{4} )}{4} + \frac{πn}{2}

x = - \frac{arcsin ( \frac{1}{4} )}{4} + \frac{πn}{2}

Solve

4 x = π + arcsin (\frac{1}{4}) + 2 πn : x = \frac{π}{4} + \frac{arcsin ( \frac{1}{4} )}{4} + \frac{πn}{2}

4 x = π + arcsin (\frac{1}{4}) + 2 πn

Divide both sides by

4

4 x = π + arcsin (\frac{1}{4}) + 2 πn

Divide both sides by

4

\frac{4 x}{4} = \frac{π}{4} + \frac{arcsin ( \frac{1}{4} )}{4} + \frac{2 πn}{4}

Simplify

x = \frac{π}{4} + \frac{arcsin ( \frac{1}{4} )}{4} + \frac{πn}{2}

x = \frac{π}{4} + \frac{arcsin ( \frac{1}{4} )}{4} + \frac{πn}{2}

x = - \frac{arcsin ( \frac{1}{4} )}{4} + \frac{πn}{2}, x = \frac{π}{4} + \frac{arcsin ( \frac{1}{4} )}{4} + \frac{πn}{2}

Show solutions in decimal form

x = - \frac{0.25268 \dots}{4} + \frac{πn}{2}, x = \frac{π}{4} + \frac{0.25268 \dots}{4} + \frac{πn}{2}

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Frequently Asked Questions (FAQ)

What is the general solution for 2=-8*sin(4x) ?
The general solution for 2=-8*sin(4x) is x=-(0.25268…)/4+(pin)/2 ,x= pi/4+(0.25268…)/4+(pin)/2