What is the general solution for arcsin(3x-pi)= 1/2 ?

The general solution for arcsin(3x-pi)= 1/2 is x=(sin(1/2)+pi)/3

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arcsin(3x-pi)= 1/2

arcsin (3 x - π) = \frac{1}{2}

x = \frac{sin ( \frac{1}{2} ) + π}{3}

Solution steps

arcsin (3 x - π) = \frac{1}{2}

Apply trig inverse properties

arcsin (3 x - π) = \frac{1}{2}

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

3 x - π = sin (\frac{1}{2})

3 x - π = sin (\frac{1}{2})

Solve

3 x - π = sin (\frac{1}{2}) : x = \frac{sin ( \frac{1}{2} ) + π}{3}

3 x - π = sin (\frac{1}{2})

Move

π

to the right side

3 x - π = sin (\frac{1}{2})

Add

π

to both sides

3 x - π + π = sin (\frac{1}{2}) + π

Simplify

3 x = sin (\frac{1}{2}) + π

3 x = sin (\frac{1}{2}) + π

Divide both sides by

3

3 x = sin (\frac{1}{2}) + π

Divide both sides by

3

\frac{3 x}{3} = \frac{sin ( \frac{1}{2} )}{3} + \frac{π}{3}

Simplify

\frac{3 x}{3} = \frac{sin ( \frac{1}{2} )}{3} + \frac{π}{3}

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

\frac{sin ( \frac{1}{2} )}{3} + \frac{π}{3} : \frac{sin ( \frac{1}{2} ) + π}{3}

\frac{sin ( \frac{1}{2} )}{3} + \frac{π}{3}

Since the denominators are equal, combine the fractions:

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

= \frac{sin ( \frac{1}{2} ) + π}{3}

x = \frac{sin ( \frac{1}{2} ) + π}{3}

x = \frac{sin ( \frac{1}{2} ) + π}{3}

x = \frac{sin ( \frac{1}{2} ) + π}{3}

x = \frac{sin ( \frac{1}{2} ) + π}{3}

2 cos^{2} (θ) + sin (θ) - 1 = 0

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

sin (θ) = \frac{13}{7}

sin^{2} (θ) - cos^{2} (θ) = 1

2 sin (3 θ) = 2

What is the general solution for arcsin(3x-pi)= 1/2 ?
The general solution for arcsin(3x-pi)= 1/2 is x=(sin(1/2)+pi)/3