Trigonometrie Beispiele

\frac{3}{10} \cdot (- 3 e^{- 3 \cdot 0.2} + \sin (0.2) + 3 \cos (0.2))

$\frac{3}{10} \cdot (- 3 e^{- 3 \cdot 0.2} + \sin (0.2) + 3 \cos (0.2))$

Schritt 1

Vereinfache jeden Term.

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Schritt 1.1

Mutltipliziere

- 3

$- 3$ mit

0.2

$0.2$ .

\frac{3}{10} \cdot (- 3 e^{- 0.6} + \sin (0.2) + 3 \cos (0.2))

$\frac{3}{10} \cdot (- 3 e^{- 0.6} + \sin (0.2) + 3 \cos (0.2))$

Schritt 1.2

Schreibe den Ausdruck um mithilfe der Regel des negativen Exponenten

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

$b^{- n} = \frac{1}{b^{n}}$ .

\frac{3}{10} \cdot (- 3 \frac{1}{e^{0.6}} + \sin (0.2) + 3 \cos (0.2))

$\frac{3}{10} \cdot (- 3 \frac{1}{e^{0.6}} + \sin (0.2) + 3 \cos (0.2))$

Schritt 1.3

Kombiniere

- 3

$- 3$ und

\frac{1}{e^{0.6}}

$\frac{1}{e^{0.6}}$ .

\frac{3}{10} \cdot (\frac{- 3}{e^{0.6}} + \sin (0.2) + 3 \cos (0.2))

$\frac{3}{10} \cdot (\frac{- 3}{e^{0.6}} + \sin (0.2) + 3 \cos (0.2))$

Schritt 1.4

Ziehe das Minuszeichen vor den Bruch.

\frac{3}{10} \cdot (- \frac{3}{e^{0.6}} + \sin (0.2) + 3 \cos (0.2))

$\frac{3}{10} \cdot (- \frac{3}{e^{0.6}} + \sin (0.2) + 3 \cos (0.2))$

\frac{3}{10} \cdot (- \frac{3}{e^{0.6}} + \sin (0.2) + 3 \cos (0.2))

$\frac{3}{10} \cdot (- \frac{3}{e^{0.6}} + \sin (0.2) + 3 \cos (0.2))$

Schritt 2

Wende das Distributivgesetz an.

\frac{3}{10} (- \frac{3}{e^{0.6}}) + \frac{3}{10} \sin (0.2) + \frac{3}{10} (3 \cos (0.2))

$\frac{3}{10} (- \frac{3}{e^{0.6}}) + \frac{3}{10} \sin (0.2) + \frac{3}{10} (3 \cos (0.2))$

Schritt 3

Vereinfache.

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Schritt 3.1

Multipliziere

\frac{3}{10} (- \frac{3}{e^{0.6}})

$\frac{3}{10} (- \frac{3}{e^{0.6}})$ .

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Schritt 3.1.1

Mutltipliziere

\frac{3}{10}

$\frac{3}{10}$ mit

\frac{3}{e^{0.6}}

$\frac{3}{e^{0.6}}$ .

- \frac{3 \cdot 3}{10 e^{0.6}} + \frac{3}{10} \sin (0.2) + \frac{3}{10} (3 \cos (0.2))

$- \frac{3 \cdot 3}{10 e^{0.6}} + \frac{3}{10} \sin (0.2) + \frac{3}{10} (3 \cos (0.2))$

Schritt 3.1.2

Mutltipliziere

3

$3$ mit

3

$3$ .

- \frac{9}{10 e^{0.6}} + \frac{3}{10} \sin (0.2) + \frac{3}{10} (3 \cos (0.2))

$- \frac{9}{10 e^{0.6}} + \frac{3}{10} \sin (0.2) + \frac{3}{10} (3 \cos (0.2))$

- \frac{9}{10 e^{0.6}} + \frac{3}{10} \sin (0.2) + \frac{3}{10} (3 \cos (0.2))

$- \frac{9}{10 e^{0.6}} + \frac{3}{10} \sin (0.2) + \frac{3}{10} (3 \cos (0.2))$

Schritt 3.2

Kombiniere

\frac{3}{10}

$\frac{3}{10}$ und

\sin (0.2)

$\sin (0.2)$ .

- \frac{9}{10 e^{0.6}} + \frac{3 \sin (0.2)}{10} + \frac{3}{10} (3 \cos (0.2))

$- \frac{9}{10 e^{0.6}} + \frac{3 \sin (0.2)}{10} + \frac{3}{10} (3 \cos (0.2))$

Schritt 3.3

Multipliziere

\frac{3}{10} (3 \cos (0.2))

$\frac{3}{10} (3 \cos (0.2))$ .

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Schritt 3.3.1

Kombiniere

3

$3$ und

\frac{3}{10}

$\frac{3}{10}$ .

- \frac{9}{10 e^{0.6}} + \frac{3 \sin (0.2)}{10} + \frac{3 \cdot 3}{10} \cos (0.2)

$- \frac{9}{10 e^{0.6}} + \frac{3 \sin (0.2)}{10} + \frac{3 \cdot 3}{10} \cos (0.2)$

Schritt 3.3.2

Mutltipliziere

3

$3$ mit

3

$3$ .

- \frac{9}{10 e^{0.6}} + \frac{3 \sin (0.2)}{10} + \frac{9}{10} \cos (0.2)

$- \frac{9}{10 e^{0.6}} + \frac{3 \sin (0.2)}{10} + \frac{9}{10} \cos (0.2)$

Schritt 3.3.3

Kombiniere

\frac{9}{10}

$\frac{9}{10}$ und

\cos (0.2)

$\cos (0.2)$ .

- \frac{9}{10 e^{0.6}} + \frac{3 \sin (0.2)}{10} + \frac{9 \cos (0.2)}{10}

$- \frac{9}{10 e^{0.6}} + \frac{3 \sin (0.2)}{10} + \frac{9 \cos (0.2)}{10}$

- \frac{9}{10 e^{0.6}} + \frac{3 \sin (0.2)}{10} + \frac{9 \cos (0.2)}{10}

$- \frac{9}{10 e^{0.6}} + \frac{3 \sin (0.2)}{10} + \frac{9 \cos (0.2)}{10}$

- \frac{9}{10 e^{0.6}} + \frac{3 \sin (0.2)}{10} + \frac{9 \cos (0.2)}{10}

$- \frac{9}{10 e^{0.6}} + \frac{3 \sin (0.2)}{10} + \frac{9 \cos (0.2)}{10}$

Schritt 4

Vereinfache jeden Term.

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Schritt 4.1

Berechne

\sin (0.2)

$\sin (0.2)$ .

- \frac{9}{10 e^{0.6}} + \frac{3 \cdot 0.19866933}{10} + \frac{9 \cos (0.2)}{10}

$- \frac{9}{10 e^{0.6}} + \frac{3 \cdot 0.19866933}{10} + \frac{9 \cos (0.2)}{10}$

Schritt 4.2

Mutltipliziere

3

$3$ mit

0.19866933

$0.19866933$ .

- \frac{9}{10 e^{0.6}} + \frac{0.59600799}{10} + \frac{9 \cos (0.2)}{10}

$- \frac{9}{10 e^{0.6}} + \frac{0.59600799}{10} + \frac{9 \cos (0.2)}{10}$

Schritt 4.3

Dividiere

0.59600799

$0.59600799$ durch

10

$10$ .

- \frac{9}{10 e^{0.6}} + 0.05960079 + \frac{9 \cos (0.2)}{10}

$- \frac{9}{10 e^{0.6}} + 0.05960079 + \frac{9 \cos (0.2)}{10}$

Schritt 4.4

Berechne

\cos (0.2)

$\cos (0.2)$ .

- \frac{9}{10 e^{0.6}} + 0.05960079 + \frac{9 \cdot 0.98006657}{10}

$- \frac{9}{10 e^{0.6}} + 0.05960079 + \frac{9 \cdot 0.98006657}{10}$

Schritt 4.5

Mutltipliziere

9

$9$ mit

0.98006657

$0.98006657$ .

- \frac{9}{10 e^{0.6}} + 0.05960079 + \frac{8.8205992}{10}

$- \frac{9}{10 e^{0.6}} + 0.05960079 + \frac{8.8205992}{10}$

Schritt 4.6

Dividiere

8.8205992

$8.8205992$ durch

10

$10$ .

- \frac{9}{10 e^{0.6}} + 0.05960079 + 0.88205992

$- \frac{9}{10 e^{0.6}} + 0.05960079 + 0.88205992$

- \frac{9}{10 e^{0.6}} + 0.05960079 + 0.88205992

$- \frac{9}{10 e^{0.6}} + 0.05960079 + 0.88205992$

Schritt 5

Vereinfache durch Addieren von Termen.

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Schritt 5.1

Addiere

- \frac{9}{10 e^{0.6}}

$- \frac{9}{10 e^{0.6}}$ und

0.05960079

$0.05960079$ .

- 0.43432967 + 0.88205992

$- 0.43432967 + 0.88205992$

Schritt 5.2

Addiere

- 0.43432967

$- 0.43432967$ und

0.88205992

$0.88205992$ .

0.44773024

$0.44773024$

0.44773024

$0.44773024$