What is the value of sinh(1.275) ?

The value of sinh(1.275) is (e^{51/20}-1)/(2e^{51/40)}

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sinh(1.275)

sinh (1.275)

\frac{e ^{\frac{51}{20}} - 1}{2 e ^{\frac{51}{40}}}

Decimal Notation

1.64963 \dots

Solution steps

sinh (1.275)

= sinh (\frac{51}{40})

Rewrite using trig identities:

\frac{e ^{\frac{51}{20}} - 1}{2 e ^{\frac{51}{40}}}

sinh (\frac{51}{40})

Use the Hyperbolic identity:

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

= \frac{e ^{\frac{51}{40}} - e ^{- \frac{51}{40}}}{2}

\frac{e ^{\frac{51}{40}} - e ^{- \frac{51}{40}}}{2} = \frac{e ^{\frac{51}{20}} - 1}{2 e ^{\frac{51}{40}}}

\frac{e ^{\frac{51}{40}} - e ^{- \frac{51}{40}}}{2}

Apply exponent rule:

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

= \frac{e ^{\frac{51}{40}} - \frac{1}{e ^{\frac{51}{40}}}}{2}

Join

e^{\frac{51}{40}} - \frac{1}{e ^{\frac{51}{40}}} : \frac{e ^{\frac{51}{20}} - 1}{e ^{\frac{51}{40}}}

e^{\frac{51}{40}} - \frac{1}{e ^{\frac{51}{40}}}

Convert element to fraction:

e^{\frac{51}{40}} = \frac{e ^{\frac{51}{40}} e ^{\frac{51}{40}}}{e ^{\frac{51}{40}}}

= \frac{e ^{\frac{51}{40}} e ^{\frac{51}{40}}}{e ^{\frac{51}{40}}} - \frac{1}{e ^{\frac{51}{40}}}

Since the denominators are equal, combine the fractions:

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

= \frac{e ^{\frac{51}{40}} e ^{\frac{51}{40}} - 1}{e ^{\frac{51}{40}}}

e^{\frac{51}{40}} e^{\frac{51}{40}} - 1 = e^{2 \cdot \frac{51}{40}} - 1

e^{\frac{51}{40}} e^{\frac{51}{40}} - 1

e^{\frac{51}{40}} e^{\frac{51}{40}} = e^{2 \cdot \frac{51}{40}}

e^{\frac{51}{40}} e^{\frac{51}{40}}

Apply exponent rule:

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

e^{\frac{51}{40}} e^{\frac{51}{40}} = e^{\frac{51}{40} + \frac{51}{40}}

= e^{\frac{51}{40} + \frac{51}{40}}

Add similar elements:

\frac{51}{40} + \frac{51}{40} = 2 \cdot \frac{51}{40}

= e^{2 \cdot \frac{51}{40}}

= e^{2 \cdot \frac{51}{40}} - 1

= \frac{e ^{2 \cdot \frac{51}{40}} - 1}{e ^{\frac{51}{40}}}

Multiply

2 \cdot \frac{51}{40} : \frac{51}{20}

2 \cdot \frac{51}{40}

Multiply fractions:

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

= \frac{51 \cdot 2}{40}

Multiply the numbers:

51 \cdot 2 = 102

= \frac{102}{40}

Cancel the common factor:

2

= \frac{51}{20}

= \frac{e ^{\frac{51}{20}} - 1}{e ^{\frac{51}{40}}}

= \frac{\frac{e ^{\frac{51}{20}} - 1}{e ^{\frac{51}{40}}}}{2}

Apply the fraction rule:

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

= \frac{e ^{\frac{51}{20}} - 1}{e ^{\frac{51}{40}} \cdot 2}

= \frac{e ^{\frac{51}{20}} - 1}{2 e ^{\frac{51}{40}}}

= \frac{e ^{\frac{51}{20}} - 1}{2 e ^{\frac{51}{40}}}

22 cos (3 0^{\circ})

arctan (\frac{20}{25})

sec (69 0^{\circ})

csc (arctan (\frac{3}{4}))

arccos (\frac{2}{21})

What is the value of sinh(1.275) ?
The value of sinh(1.275) is (e^{51/20}-1)/(2e^{51/40)}