What is the value of sinh(7/20) ?

The value of sinh(7/20) is (e^{7/10}-1)/(2e^{7/20)}

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sinh(7/20)

sinh (\frac{7}{20})

\frac{e ^{\frac{7}{10}} - 1}{2 e ^{\frac{7}{20}}}

Decimal Notation

0.35718 \dots

Solution steps

sinh (\frac{7}{20})

Use the Hyperbolic identity:

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

= \frac{e ^{\frac{7}{20}} - e ^{- \frac{7}{20}}}{2}

\frac{e ^{\frac{7}{20}} - e ^{- \frac{7}{20}}}{2} = \frac{e ^{\frac{7}{10}} - 1}{2 e ^{\frac{7}{20}}}

\frac{e ^{\frac{7}{20}} - e ^{- \frac{7}{20}}}{2}

Apply exponent rule:

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

= \frac{e ^{\frac{7}{20}} - \frac{1}{e ^{\frac{7}{20}}}}{2}

Join

e^{\frac{7}{20}} - \frac{1}{e ^{\frac{7}{20}}} : \frac{e ^{\frac{7}{10}} - 1}{e ^{\frac{7}{20}}}

e^{\frac{7}{20}} - \frac{1}{e ^{\frac{7}{20}}}

Convert element to fraction:

e^{\frac{7}{20}} = \frac{e ^{\frac{7}{20}} e ^{\frac{7}{20}}}{e ^{\frac{7}{20}}}

= \frac{e ^{\frac{7}{20}} e ^{\frac{7}{20}}}{e ^{\frac{7}{20}}} - \frac{1}{e ^{\frac{7}{20}}}

Since the denominators are equal, combine the fractions:

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

= \frac{e ^{\frac{7}{20}} e ^{\frac{7}{20}} - 1}{e ^{\frac{7}{20}}}

e^{\frac{7}{20}} e^{\frac{7}{20}} - 1 = e^{2 \cdot \frac{7}{20}} - 1

e^{\frac{7}{20}} e^{\frac{7}{20}} - 1

e^{\frac{7}{20}} e^{\frac{7}{20}} = e^{2 \cdot \frac{7}{20}}

e^{\frac{7}{20}} e^{\frac{7}{20}}

Apply exponent rule:

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

e^{\frac{7}{20}} e^{\frac{7}{20}} = e^{\frac{7}{20} + \frac{7}{20}}

= e^{\frac{7}{20} + \frac{7}{20}}

Add similar elements:

\frac{7}{20} + \frac{7}{20} = 2 \cdot \frac{7}{20}

= e^{2 \cdot \frac{7}{20}}

= e^{2 \cdot \frac{7}{20}} - 1

= \frac{e ^{2 \cdot \frac{7}{20}} - 1}{e ^{\frac{7}{20}}}

Multiply

2 \cdot \frac{7}{20} : \frac{7}{10}

2 \cdot \frac{7}{20}

Multiply fractions:

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

= \frac{7 \cdot 2}{20}

Multiply the numbers:

7 \cdot 2 = 14

= \frac{14}{20}

Cancel the common factor:

2

= \frac{7}{10}

= \frac{e ^{\frac{7}{10}} - 1}{e ^{\frac{7}{20}}}

= \frac{\frac{e ^{\frac{7}{10}} - 1}{e ^{\frac{7}{20}}}}{2}

Apply the fraction rule:

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

= \frac{e ^{\frac{7}{10}} - 1}{e ^{\frac{7}{20}} \cdot 2}

= \frac{e ^{\frac{7}{10}} - 1}{2 e ^{\frac{7}{20}}}

sin (4 5^{\circ}) + tan (3 0^{\circ})

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What is the value of sinh(7/20) ?
The value of sinh(7/20) is (e^{7/10}-1)/(2e^{7/20)}