What is the general solution for -6arcsin(3x)=pi ?

The general solution for -6arcsin(3x)=pi is x=-1/6

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-6arcsin(3x)=pi

- 6 arcsin (3 x) = π

x = - \frac{1}{6}

Solution steps

- 6 arcsin (3 x) = π

Divide both sides by

- 6

- 6 arcsin (3 x) = π

Divide both sides by

- 6

\frac{- 6 arcsin ( 3 x )}{- 6} = \frac{π}{- 6}

Simplify

arcsin (3 x) = - \frac{π}{6}

arcsin (3 x) = - \frac{π}{6}

Apply trig inverse properties

arcsin (3 x) = - \frac{π}{6}

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

3 x = sin (- \frac{π}{6})

sin (- \frac{π}{6}) = - \frac{1}{2}

sin (- \frac{π}{6})

Use the following property:

sin (- x) = - sin (x)

sin (- \frac{π}{6}) = - sin (\frac{π}{6})

= - sin (\frac{π}{6})

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

sin (\frac{π}{6})

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{1}{2}

= - \frac{1}{2}

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

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

Solve

3 x = - \frac{1}{2} : x = - \frac{1}{6}

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

Divide both sides by

3

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

Divide both sides by

3

\frac{3 x}{3} = \frac{- \frac{1}{2}}{3}

Simplify

\frac{3 x}{3} = \frac{- \frac{1}{2}}{3}

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

\frac{- \frac{1}{2}}{3} : - \frac{1}{6}

\frac{- \frac{1}{2}}{3}

Apply the fraction rule:

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

= - \frac{\frac{1}{2}}{3}

Apply the fraction rule:

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

\frac{\frac{1}{2}}{3} = \frac{1}{2 \cdot 3}

= - \frac{1}{2 \cdot 3}

Multiply the numbers:

2 \cdot 3 = 6

= - \frac{1}{6}

x = - \frac{1}{6}

x = - \frac{1}{6}

x = - \frac{1}{6}

x = - \frac{1}{6}

tan^{2} (p) = tan (p)

sin (x) + cos (x) = \frac{2}{3}

2 cos^{2} (2 θ) = 1 - cos (2 θ)

1 + tan^{2} (x) = 0

sin (x) = \frac{3}{8}

What is the general solution for -6arcsin(3x)=pi ?
The general solution for -6arcsin(3x)=pi is x=-1/6