What is the inverse of (arcsin(x/3-7/6))/2+(3pi)/2 ?

The inverse of (arcsin(x/3-7/6))/2+(3pi)/2 is 3sin(2x-3pi)+7/2

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inverse of (arcsin(x/3-7/6))/2+(3pi)/2

inverse

\frac{arcsin ( \frac{x}{3} - \frac{7}{6} )}{2} + \frac{3 π}{2}

3 sin (2 x - 3 π) + \frac{7}{2}

Solution steps

Solve for

arcsin (\frac{x}{3} - \frac{7}{6}), y = \frac{arcsin ( \frac{x}{3} - \frac{7}{6} )}{2} + \frac{3 π}{2}

arcsin (\frac{x}{3} - \frac{7}{6}) = 2 y - 3 π

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

\frac{x}{3} - \frac{7}{6} = sin (2 y - 3 π)

Solve for

x, \frac{x}{3} - \frac{7}{6} = sin (2 y - 3 π)

3 sin (2 y - 3 π) + \frac{7}{2}

Substitute

y = x

3 sin (2 x - 3 π) + \frac{7}{2}

tan (\frac{7.5}{4})

f (x) = \frac{x + 5}{4 x}

\frac{x ^{3}}{6}

f (x) = 2 (x + 125)^{2} - 31250

\frac{D}{D x} 8 x^{3} - 15 x^{2} - 2

What is the inverse of (arcsin(x/3-7/6))/2+(3pi)/2 ?
The inverse of (arcsin(x/3-7/6))/2+(3pi)/2 is 3sin(2x-3pi)+7/2