What is the value of sinh(7) ?

The value of sinh(7) is (e^{14}-1)/(2e^7)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sinh(7)

sinh (7)

\frac{e ^{14} - 1}{2 e ^{7}}

Decimal Notation

548.31612 \dots

Solution steps

sinh (7)

Use the Hyperbolic identity:

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

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

\frac{e ^{7} - e ^{- 7}}{2} = \frac{e ^{14} - 1}{2 e ^{7}}

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

Apply exponent rule:

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

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

Join

e^{7} - \frac{1}{e ^{7}} : \frac{e ^{14} - 1}{e ^{7}}

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

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

e^{7} e^{7} - 1 = e^{14} - 1

e^{7} e^{7} - 1

e^{7} e^{7} = e^{14}

e^{7} e^{7}

Apply exponent rule:

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

e^{7} e^{7} = e^{7 + 7}

= e^{7 + 7}

Add the numbers:

7 + 7 = 14

= e^{14}

= e^{14} - 1

= \frac{e ^{14} - 1}{e ^{7}}

= \frac{\frac{e ^{14} - 1}{e ^{7}}}{2}

Apply the fraction rule:

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

= \frac{e ^{14} - 1}{e ^{7} \cdot 2}

= \frac{e ^{14} - 1}{2 e ^{7}}

arccos (\frac{8}{4})

cos (0) e^{0}

csc (8 6^{\circ})

180 + arctan (\frac{- 1}{- 1})

tan (- 1) (\frac{- 0.756}{- 0.864})