What is the value of sinh(4) ?

The value of sinh(4) is (e^8-1)/(2e^4)

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sinh(4)

sinh (4)

\frac{e ^{8} - 1}{2 e ^{4}}

Decimal Notation

27.28991 \dots

Solution steps

sinh (4)

Use the Hyperbolic identity:

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

= \frac{e ^{4} - e ^{- 4}}{2}

\frac{e ^{4} - e ^{- 4}}{2} = \frac{e ^{8} - 1}{2 e ^{4}}

\frac{e ^{4} - e ^{- 4}}{2}

Apply exponent rule:

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

= \frac{e ^{4} - \frac{1}{e ^{4}}}{2}

Join

e^{4} - \frac{1}{e ^{4}} : \frac{e ^{8} - 1}{e ^{4}}

e^{4} - \frac{1}{e ^{4}}

Convert element to fraction:

e^{4} = \frac{e ^{4} e ^{4}}{e ^{4}}

= \frac{e ^{4} e ^{4}}{e ^{4}} - \frac{1}{e ^{4}}

Since the denominators are equal, combine the fractions:

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

= \frac{e ^{4} e ^{4} - 1}{e ^{4}}

e^{4} e^{4} - 1 = e^{8} - 1

e^{4} e^{4} - 1

e^{4} e^{4} = e^{8}

e^{4} e^{4}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{4} e^{4} = e^{4 + 4}

= e^{4 + 4}

Add the numbers:

4 + 4 = 8

= e^{8}

= e^{8} - 1

= \frac{e ^{8} - 1}{e ^{4}}

= \frac{\frac{e ^{8} - 1}{e ^{4}}}{2}

Apply the fraction rule:

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

= \frac{e ^{8} - 1}{e ^{4} \cdot 2}

= \frac{e ^{8} - 1}{2 e ^{4}}

arctan (\frac{4}{4})

cot (36 0^{\circ})

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tan (- 18 0^{\circ})

arccos (cos (- \frac{π}{3}))