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cosh(0.6)

Lösung

cosh (0.6)

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

Dezimale

1.18546 \dots

Schritte zur Lösung

cosh (0.6)

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

Umschreiben mit Hilfe von Trigonometrie-Identitäten:

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

cosh (\frac{3}{5})

Hyperbolische Identität anwenden:

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}

Wende Exponentenregel an:

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

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

Füge

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

zusammen:

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

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

Wandle das Element in einen Bruch um:

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}}}

Da die Nenner gleich sind, fasse die Brüche zusammen.:

\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}}

Wende Exponentenregel an:

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}}

Addiere gleiche Elemente:

\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}}}

Multipliziere

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

2 \cdot \frac{3}{5}

Multipliziere Brüche:

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

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

Multipliziere die Zahlen:

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}

Wende Bruchregel an:

\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}))

sec^{5} (0)

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

- 2 cos (- 1)