What is the value of cosh(0.6) ?

The value of cosh(0.6) is (e^{6/5}+1)/(2e^{3/5)}

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cosh(0.6)

cosh (0.6)

\frac{e ^{\frac{6}{5}} + 1}{2 e ^{\frac{3}{5}}}

Decimal Notation

1.18546 \dots

Solution steps

cosh (0.6)

= cosh (\frac{3}{5})

Rewrite using trig identities:

\frac{e ^{\frac{6}{5}} + 1}{2 e ^{\frac{3}{5}}}

cosh (\frac{3}{5})

Use the Hyperbolic identity:

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

= \frac{e ^{\frac{3}{5}} + e ^{- \frac{3}{5}}}{2}

\frac{e ^{\frac{3}{5}} + e ^{- \frac{3}{5}}}{2} = \frac{e ^{\frac{6}{5}} + 1}{2 e ^{\frac{3}{5}}}

\frac{e ^{\frac{3}{5}} + e ^{- \frac{3}{5}}}{2}

Apply exponent rule:

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

= \frac{e ^{\frac{3}{5}} + \frac{1}{e ^{\frac{3}{5}}}}{2}

Join

e^{\frac{3}{5}} + \frac{1}{e ^{\frac{3}{5}}} : \frac{e ^{\frac{6}{5}} + 1}{e ^{\frac{3}{5}}}

e^{\frac{3}{5}} + \frac{1}{e ^{\frac{3}{5}}}

Convert element to fraction:

e^{\frac{3}{5}} = \frac{e ^{\frac{3}{5}} e ^{\frac{3}{5}}}{e ^{\frac{3}{5}}}

= \frac{e ^{\frac{3}{5}} e ^{\frac{3}{5}}}{e ^{\frac{3}{5}}} + \frac{1}{e ^{\frac{3}{5}}}

Since the denominators are equal, combine the fractions:

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

= \frac{e ^{\frac{3}{5}} e ^{\frac{3}{5}} + 1}{e ^{\frac{3}{5}}}

e^{\frac{3}{5}} e^{\frac{3}{5}} + 1 = e^{2 \cdot \frac{3}{5}} + 1

e^{\frac{3}{5}} e^{\frac{3}{5}} + 1

e^{\frac{3}{5}} e^{\frac{3}{5}} = e^{2 \cdot \frac{3}{5}}

e^{\frac{3}{5}} e^{\frac{3}{5}}

Apply exponent rule:

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

e^{\frac{3}{5}} e^{\frac{3}{5}} = e^{\frac{3}{5} + \frac{3}{5}}

= e^{\frac{3}{5} + \frac{3}{5}}

Add similar elements:

\frac{3}{5} + \frac{3}{5} = 2 \cdot \frac{3}{5}

= e^{2 \cdot \frac{3}{5}}

= e^{2 \cdot \frac{3}{5}} + 1

= \frac{e ^{2 \cdot \frac{3}{5}} + 1}{e ^{\frac{3}{5}}}

Multiply

2 \cdot \frac{3}{5} : \frac{6}{5}

2 \cdot \frac{3}{5}

Multiply fractions:

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

= \frac{3 \cdot 2}{5}

Multiply the numbers:

3 \cdot 2 = 6

= \frac{6}{5}

= \frac{e ^{\frac{6}{5}} + 1}{e ^{\frac{3}{5}}}

= \frac{\frac{e ^{\frac{6}{5}} + 1}{e ^{\frac{3}{5}}}}{2}

Apply the fraction rule:

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

= \frac{e ^{\frac{6}{5}} + 1}{e ^{\frac{3}{5}} \cdot 2}

= \frac{e ^{\frac{6}{5}} + 1}{2 e ^{\frac{3}{5}}}

= \frac{e ^{\frac{6}{5}} + 1}{2 e ^{\frac{3}{5}}}

2 sec (4 5^{\circ})

(sec (79.3 6^{\circ})) (sin (79.3 6^{\circ})) - (tan (79.3 6^{\circ}))

60 sin (4 1^{\circ})

sec^{5} (0)

- sin (\frac{π}{6}) - cos (\frac{π}{6} + \frac{π}{6})

What is the value of cosh(0.6) ?
The value of cosh(0.6) is (e^{6/5}+1)/(2e^{3/5)}