What is the value of cosh(0.5) ?

The value of cosh(0.5) is (e^{1/2}sqrt(e)+1)/(2sqrt(e))

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cosh(0.5)

cosh (0.5)

\frac{e ^{\frac{1}{2}} e + 1}{2 e}

Decimal Notation

1.12762 \dots

Solution steps

cosh (0.5)

= cosh (\frac{1}{2})

Rewrite using trig identities:

\frac{e ^{\frac{1}{2}} e + 1}{2 e}

cosh (\frac{1}{2})

Use the Hyperbolic identity:

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

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

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

\frac{e ^{\frac{1}{2}} + e ^{- \frac{1}{2}}}{2}

Apply exponent rule:

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

= \frac{e ^{\frac{1}{2}} + \frac{1}{e}}{2}

Join

e^{\frac{1}{2}} + \frac{1}{e} : \frac{e ^{\frac{1}{2}} e + 1}{e}

e^{\frac{1}{2}} + \frac{1}{e}

Convert element to fraction:

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

= \frac{e ^{\frac{1}{2}} e}{e} + \frac{1}{e}

Since the denominators are equal, combine the fractions:

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

= \frac{e ^{\frac{1}{2}} e + 1}{e}

= \frac{\frac{e ^{\frac{1}{2}} e + 1}{e}}{2}

Apply the fraction rule:

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

= \frac{e ^{\frac{1}{2}} e + 1}{e \cdot 2}

= \frac{e ^{\frac{1}{2}} e + 1}{2 e}

= \frac{e ^{\frac{1}{2}} e + 1}{2 e}

13 cos (4 0^{\circ})

arcsin (sin (\frac{9 π}{10}))

arccos (1.25)

tan (arccos (0))

cot (1.5)

What is the value of cosh(0.5) ?
The value of cosh(0.5) is (e^{1/2}sqrt(e)+1)/(2sqrt(e))