What is the value of sinh(1/2) ?

The value of sinh(1/2) is (e^{1/2}sqrt(e)-1)/(2sqrt(e))

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sinh(1/2)

sinh (\frac{1}{2})

\frac{e ^{\frac{1}{2}} e - 1}{2 e}

Decimal Notation

0.52109 \dots

Solution steps

sinh (\frac{1}{2})

Use the Hyperbolic identity:

sinh (x) = \frac{e ^{x} - e ^{- x}}{2}

= \frac{e ^{\frac{1}{2}} - e ^{- \frac{1}{2}}}{2}

\frac{e ^{\frac{1}{2}} - e ^{- \frac{1}{2}}}{2} = \frac{e ^{\frac{1}{2}} e - 1}{2 e}

\frac{e ^{\frac{1}{2}} - e ^{- \frac{1}{2}}}{2}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{e ^{\frac{1}{2}} - \frac{1}{e}}{2}

Join

e^{\frac{1}{2}} - \frac{1}{e} : \frac{e ^{\frac{1}{2}} e - 1}{e}

e^{\frac{1}{2}} - \frac{1}{e}

Convert element to fraction:

e^{\frac{1}{2}} = \frac{e ^{\frac{1}{2}} e}{e}

= \frac{e ^{\frac{1}{2}} e}{e} - \frac{1}{e}

Since the denominators are equal, combine the fractions:

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

= \frac{e ^{\frac{1}{2}} e - 1}{e}

= \frac{\frac{e ^{\frac{1}{2}} e - 1}{e}}{2}

Apply the fraction rule:

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

= \frac{e ^{\frac{1}{2}} e - 1}{e \cdot 2}

= \frac{e ^{\frac{1}{2}} e - 1}{2 e}

arccsc (\frac{5}{2})

cos^{2} (2 7^{\circ})

arctan (\frac{1.5}{3})

2 sin (\frac{- π}{2})

sec (\frac{π}{3}) tan (\frac{π}{3}) + 2 sin (\frac{π}{3})

What is the value of sinh(1/2) ?
The value of sinh(1/2) is (e^{1/2}sqrt(e)-1)/(2sqrt(e))