What is the general solution for sinh(x)= 7/24 ?

The general solution for sinh(x)= 7/24 is x=ln(4/3)

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sinh(x)= 7/24

sinh (x) = \frac{7}{24}

x = ln (\frac{4}{3})

Solution steps

sinh (x) = \frac{7}{24}

Rewrite using trig identities

\frac{e ^{x} - e ^{- x}}{2} = \frac{7}{24}

\frac{e ^{x} - e ^{- x}}{2} = \frac{7}{24} : x = ln (\frac{4}{3})

x = ln (\frac{4}{3})

cos (x) = \frac{5}{15}

cos (θ) = \frac{3}{5}, 0 < θ < \frac{π}{2}

sin (x) - cos^{2} (x) sin (x) = - 1

3 + 3 sin (x) = 2 cos^{2} (x)

(cot (θ) + 1) (csc (θ) - \frac{1}{2}) = 0

What is the general solution for sinh(x)= 7/24 ?
The general solution for sinh(x)= 7/24 is x=ln(4/3)