What is the general solution for -arcsin(4x)= pi/4 ?

The general solution for -arcsin(4x)= pi/4 is x=-1/(4sqrt(2))

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-arcsin(4x)= pi/4

Solution

- arcsin (4 x) = \frac{π}{4}

Solution

x = - \frac{1}{4 2}

Solution steps

- arcsin (4 x) = \frac{π}{4}

Divide both sides by

- 1

- arcsin (4 x) = \frac{π}{4}

Divide both sides by

- 1

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

Simplify

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

Simplify

\frac{- arcsin ( 4 x )}{- 1} : arcsin (4 x)

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

Apply the fraction rule:

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

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

Apply rule

\frac{a}{1} = a

= arcsin (4 x)

Simplify

\frac{\frac{π}{4}}{- 1} : - \frac{π}{4}

\frac{\frac{π}{4}}{- 1}

Apply the fraction rule:

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

= - \frac{\frac{π}{4}}{1}

Apply the fraction rule:

\frac{a}{1} = a

\frac{\frac{π}{4}}{1} = \frac{π}{4}

= - \frac{π}{4}

arcsin (4 x) = - \frac{π}{4}

arcsin (4 x) = - \frac{π}{4}

arcsin (4 x) = - \frac{π}{4}

Apply trig inverse properties

arcsin (4 x) = - \frac{π}{4}

arcsin (x) = a \Rightarrow x = sin (a)

4 x = sin (- \frac{π}{4})

sin (- \frac{π}{4}) = - \frac{2}{2}

sin (- \frac{π}{4})

Use the following property:

sin (- x) = - sin (x)

sin (- \frac{π}{4}) = - sin (\frac{π}{4})

= - sin (\frac{π}{4})

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

sin (\frac{π}{4})

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}

= \frac{2}{2}

= - \frac{2}{2}

4 x = - \frac{2}{2}

4 x = - \frac{2}{2}

Solve

4 x = - \frac{2}{2} : x = - \frac{1}{4 2}

4 x = - \frac{2}{2}

Apply radical rule:

a = a a

2 = 22

4 x = - \frac{2}{2 2}

Cancel the common factor:

2

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

Divide both sides by

4

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

Divide both sides by

4

\frac{4 x}{4} = \frac{- \frac{1}{2}}{4}

Simplify

\frac{4 x}{4} = \frac{- \frac{1}{2}}{4}

Simplify

\frac{4 x}{4} : x

\frac{4 x}{4}

Divide the numbers:

\frac{4}{4} = 1

= x

Simplify

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

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

Apply the fraction rule:

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

= - \frac{\frac{1}{2}}{4}

Apply the fraction rule:

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

\frac{\frac{1}{2}}{4} = \frac{1}{2 \cdot 4}

= - \frac{1}{2 \cdot 4}

x = - \frac{1}{4 2}

x = - \frac{1}{4 2}

x = - \frac{1}{4 2}

x = - \frac{1}{4 2}

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Frequently Asked Questions (FAQ)

What is the general solution for -arcsin(4x)= pi/4 ?
The general solution for -arcsin(4x)= pi/4 is x=-1/(4sqrt(2))