What is the general solution for -3arcsin(2x)=pi ?

The general solution for -3arcsin(2x)=pi is x=-(sqrt(3))/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

-3arcsin(2x)=pi

- 3 arcsin (2 x) = π

x = - \frac{3}{4}

Solution steps

- 3 arcsin (2 x) = π

Divide both sides by

- 3

- 3 arcsin (2 x) = π

Divide both sides by

- 3

\frac{- 3 arcsin ( 2 x )}{- 3} = \frac{π}{- 3}

Simplify

arcsin (2 x) = - \frac{π}{3}

arcsin (2 x) = - \frac{π}{3}

Apply trig inverse properties

arcsin (2 x) = - \frac{π}{3}

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

2 x = sin (- \frac{π}{3})

sin (- \frac{π}{3}) = - \frac{3}{2}

sin (- \frac{π}{3})

Use the following property:

sin (- x) = - sin (x)

sin (- \frac{π}{3}) = - sin (\frac{π}{3})

= - sin (\frac{π}{3})

Use the following trivial identity:

sin (\frac{π}{3}) = \frac{3}{2}

sin (\frac{π}{3})

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{3}{2}

= - \frac{3}{2}

2 x = - \frac{3}{2}

2 x = - \frac{3}{2}

Solve

2 x = - \frac{3}{2} : x = - \frac{3}{4}

2 x = - \frac{3}{2}

Divide both sides by

2

2 x = - \frac{3}{2}

Divide both sides by

2

\frac{2 x}{2} = \frac{- \frac{3}{2}}{2}

Simplify

\frac{2 x}{2} = \frac{- \frac{3}{2}}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{- \frac{3}{2}}{2} : - \frac{3}{4}

\frac{- \frac{3}{2}}{2}

Apply the fraction rule:

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

= - \frac{\frac{3}{2}}{2}

Apply the fraction rule:

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

\frac{\frac{3}{2}}{2} = \frac{3}{2 \cdot 2}

= - \frac{3}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= - \frac{3}{4}

x = - \frac{3}{4}

x = - \frac{3}{4}

x = - \frac{3}{4}

x = - \frac{3}{4}

3 tan (3 x) = 3

\frac{1}{2} + cos (θ) = 0

(2 cos (x) - 1) (2 sin (x) + 3) = 0

2 sin (2 x) = 2 cos (x)

tan (\frac{1}{2} x) + 1 = 0

What is the general solution for -3arcsin(2x)=pi ?
The general solution for -3arcsin(2x)=pi is x=-(sqrt(3))/4