What is the value of sinh(7/18) ?

The value of sinh(7/18) is (e^{7/9}-1)/(2e^{7/18)}

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sinh(7/18)

sinh (\frac{7}{18})

\frac{e ^{\frac{7}{9}} - 1}{2 e ^{\frac{7}{18}}}

Decimal Notation

0.39876 \dots

Solution steps

sinh (\frac{7}{18})

Use the Hyperbolic identity:

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

= \frac{e ^{\frac{7}{18}} - e ^{- \frac{7}{18}}}{2}

\frac{e ^{\frac{7}{18}} - e ^{- \frac{7}{18}}}{2} = \frac{e ^{\frac{7}{9}} - 1}{2 e ^{\frac{7}{18}}}

\frac{e ^{\frac{7}{18}} - e ^{- \frac{7}{18}}}{2}

Apply exponent rule:

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

= \frac{e ^{\frac{7}{18}} - \frac{1}{e ^{\frac{7}{18}}}}{2}

Join

e^{\frac{7}{18}} - \frac{1}{e ^{\frac{7}{18}}} : \frac{e ^{\frac{7}{9}} - 1}{e ^{\frac{7}{18}}}

e^{\frac{7}{18}} - \frac{1}{e ^{\frac{7}{18}}}

Convert element to fraction:

e^{\frac{7}{18}} = \frac{e ^{\frac{7}{18}} e ^{\frac{7}{18}}}{e ^{\frac{7}{18}}}

= \frac{e ^{\frac{7}{18}} e ^{\frac{7}{18}}}{e ^{\frac{7}{18}}} - \frac{1}{e ^{\frac{7}{18}}}

Since the denominators are equal, combine the fractions:

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

= \frac{e ^{\frac{7}{18}} e ^{\frac{7}{18}} - 1}{e ^{\frac{7}{18}}}

e^{\frac{7}{18}} e^{\frac{7}{18}} - 1 = e^{2 \cdot \frac{7}{18}} - 1

e^{\frac{7}{18}} e^{\frac{7}{18}} - 1

e^{\frac{7}{18}} e^{\frac{7}{18}} = e^{2 \cdot \frac{7}{18}}

e^{\frac{7}{18}} e^{\frac{7}{18}}

Apply exponent rule:

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

e^{\frac{7}{18}} e^{\frac{7}{18}} = e^{\frac{7}{18} + \frac{7}{18}}

= e^{\frac{7}{18} + \frac{7}{18}}

Add similar elements:

\frac{7}{18} + \frac{7}{18} = 2 \cdot \frac{7}{18}

= e^{2 \cdot \frac{7}{18}}

= e^{2 \cdot \frac{7}{18}} - 1

= \frac{e ^{2 \cdot \frac{7}{18}} - 1}{e ^{\frac{7}{18}}}

Multiply

2 \cdot \frac{7}{18} : \frac{7}{9}

2 \cdot \frac{7}{18}

Multiply fractions:

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

= \frac{7 \cdot 2}{18}

Multiply the numbers:

7 \cdot 2 = 14

= \frac{14}{18}

Cancel the common factor:

2

= \frac{7}{9}

= \frac{e ^{\frac{7}{9}} - 1}{e ^{\frac{7}{18}}}

= \frac{\frac{e ^{\frac{7}{9}} - 1}{e ^{\frac{7}{18}}}}{2}

Apply the fraction rule:

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

= \frac{e ^{\frac{7}{9}} - 1}{e ^{\frac{7}{18}} \cdot 2}

= \frac{e ^{\frac{7}{9}} - 1}{2 e ^{\frac{7}{18}}}

190 cos (2 0^{\circ})

9 arccos (- 1)

cos (\frac{2 π}{3} + \frac{3 π}{4})

cos (arctan (0))

10 \cdot cos (5 0^{\circ})

What is the value of sinh(7/18) ?
The value of sinh(7/18) is (e^{7/9}-1)/(2e^{7/18)}