What is the general solution for 2=3sin(|5x|)+1 ?

The general solution for 2=3sin(|5x|)+1 is No Solution for x\in\mathbb{R}

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Popular >

2=3sin(|5x|)+1

Solution

2 = 3 sin (∣ 5 x ∣) + 1

Solution

No Solution for x \in R

Solution steps

2 = 3 sin (∣ 5 x ∣) + 1

Switch sides

3 sin (∣ 5 x ∣) + 1 = 2

Move

1

to the right side

3 sin (∣ 5 x ∣) + 1 = 2

Subtract

1

from both sides

3 sin (∣ 5 x ∣) + 1 - 1 = 2 - 1

Simplify

3 sin (∣ 5 x ∣) = 1

3 sin (∣ 5 x ∣) = 1

Divide both sides by

3

3 sin (∣ 5 x ∣) = 1

Divide both sides by

3

\frac{3 sin ( ∣ 5 x ∣ )}{3} = \frac{1}{3}

Simplify

sin (∣ 5 x ∣) = \frac{1}{3}

sin (∣ 5 x ∣) = \frac{1}{3}

Apply trig inverse properties

sin (∣ 5 x ∣) = \frac{1}{3}

General solutions for

sin (∣ 5 x ∣) = \frac{1}{3}

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

∣ 5 x ∣ = arcsin (\frac{1}{3}) + 2 πn, ∣ 5 x ∣ = π - arcsin (\frac{1}{3}) + 2 πn

∣ 5 x ∣ = arcsin (\frac{1}{3}) + 2 πn, ∣ 5 x ∣ = π - arcsin (\frac{1}{3}) + 2 πn

Solve

∣ 5 x ∣ = arcsin (\frac{1}{3}) + 2 πn :

No Solution

∣ 5 x ∣ = arcsin (\frac{1}{3}) + 2 πn

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

u = - a

5 x = - (arcsin (\frac{1}{3}) + 2 πn) or 5 x = arcsin (\frac{1}{3}) + 2 πn

5 x = - (arcsin (\frac{1}{3}) + 2 πn) or 5 x = arcsin (\frac{1}{3}) + 2 πn

5 x = - (arcsin (\frac{1}{3}) + 2 πn) or 5 x = arcsin (\frac{1}{3}) + 2 πn

5 x = - (arcsin (\frac{1}{3}) + 2 πn) : x = - \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

5 x = - (arcsin (\frac{1}{3}) + 2 πn)

Divide both sides by

5

5 x = - (arcsin (\frac{1}{3}) + 2 πn)

Divide both sides by

5

\frac{5 x}{5} = \frac{- ( arcsin ( \frac{1}{3} ) + 2 πn )}{5}

Simplify

\frac{5 x}{5} = \frac{- ( arcsin ( \frac{1}{3} ) + 2 πn )}{5}

Simplify

\frac{5 x}{5} : x

\frac{5 x}{5}

Divide the numbers:

\frac{5}{5} = 1

= x

Simplify

\frac{- ( arcsin ( \frac{1}{3} ) + 2 πn )}{5} : - \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

\frac{- ( arcsin ( \frac{1}{3} ) + 2 πn )}{5}

Apply the fraction rule:

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

= - \frac{( arcsin ( \frac{1}{3} ) + 2 πn )}{5}

Remove parentheses:

(a) = a

= - \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = - \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = - \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = - \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

5 x = arcsin (\frac{1}{3}) + 2 πn : x = \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

5 x = arcsin (\frac{1}{3}) + 2 πn

Divide both sides by

5

5 x = arcsin (\frac{1}{3}) + 2 πn

Divide both sides by

5

\frac{5 x}{5} = \frac{arcsin ( \frac{1}{3} )}{5} + \frac{2 πn}{5}

Simplify

\frac{5 x}{5} = \frac{arcsin ( \frac{1}{3} )}{5} + \frac{2 πn}{5}

Simplify

\frac{5 x}{5} : x

\frac{5 x}{5}

Divide the numbers:

\frac{5}{5} = 1

= x

Simplify

\frac{arcsin ( \frac{1}{3} )}{5} + \frac{2 πn}{5} : \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

\frac{arcsin ( \frac{1}{3} )}{5} + \frac{2 πn}{5}

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

Combine Solutions:

No Solution or No Solution

No Solution or No Solution

No Solution for x \in R

Solve

∣ 5 x ∣ = π - arcsin (\frac{1}{3}) + 2 πn :

No Solution

∣ 5 x ∣ = π - arcsin (\frac{1}{3}) + 2 πn

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

u = - a

5 x = - (π - arcsin (\frac{1}{3}) + 2 πn) or 5 x = π - arcsin (\frac{1}{3}) + 2 πn

5 x = - (π - arcsin (\frac{1}{3}) + 2 πn) or 5 x = π - arcsin (\frac{1}{3}) + 2 πn

5 x = - (π - arcsin (\frac{1}{3}) + 2 πn) or 5 x = π - arcsin (\frac{1}{3}) + 2 πn

5 x = - (π - arcsin (\frac{1}{3}) + 2 πn) : x = - \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

5 x = - (π - arcsin (\frac{1}{3}) + 2 πn)

Divide both sides by

5

5 x = - (π - arcsin (\frac{1}{3}) + 2 πn)

Divide both sides by

5

\frac{5 x}{5} = \frac{- ( π - arcsin ( \frac{1}{3} ) + 2 πn )}{5}

Simplify

\frac{5 x}{5} = \frac{- ( π - arcsin ( \frac{1}{3} ) + 2 πn )}{5}

Simplify

\frac{5 x}{5} : x

\frac{5 x}{5}

Divide the numbers:

\frac{5}{5} = 1

= x

Simplify

\frac{- ( π - arcsin ( \frac{1}{3} ) + 2 πn )}{5} : - \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

\frac{- ( π - arcsin ( \frac{1}{3} ) + 2 πn )}{5}

Apply the fraction rule:

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

= - \frac{( π - arcsin ( \frac{1}{3} ) + 2 πn )}{5}

Remove parentheses:

(a) = a

= - \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = - \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = - \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = - \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

5 x = π - arcsin (\frac{1}{3}) + 2 πn : x = \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

5 x = π - arcsin (\frac{1}{3}) + 2 πn

Divide both sides by

5

5 x = π - arcsin (\frac{1}{3}) + 2 πn

Divide both sides by

5

\frac{5 x}{5} = \frac{π}{5} - \frac{arcsin ( \frac{1}{3} )}{5} + \frac{2 πn}{5}

Simplify

\frac{5 x}{5} = \frac{π}{5} - \frac{arcsin ( \frac{1}{3} )}{5} + \frac{2 πn}{5}

Simplify

\frac{5 x}{5} : x

\frac{5 x}{5}

Divide the numbers:

\frac{5}{5} = 1

= x

Simplify

\frac{π}{5} - \frac{arcsin ( \frac{1}{3} )}{5} + \frac{2 πn}{5} : \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

\frac{π}{5} - \frac{arcsin ( \frac{1}{3} )}{5} + \frac{2 πn}{5}

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

Combine Solutions:

No Solution or No Solution

No Solution or No Solution

No Solution for x \in R

x = No Solution, x = No Solution

Since the equation is undefined for:

No Solution

No Solution for x \in R

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Frequently Asked Questions (FAQ)

What is the general solution for 2=3sin(|5x|)+1 ?
The general solution for 2=3sin(|5x|)+1 is No Solution for x\in\mathbb{R}