Trigonometria Exemplos

$(\sin (x + 1)) (\sin (x - 1))$

Etapa 1

Double negation

$\sin (x - (- 1)) \sin (x - 1)$

Etapa 2

Aplique a fórmula da diferença dos ângulos.

$(\sin (x) \cos (- 1) - \cos (x) \sin (- 1)) \sin (x - 1)$

Etapa 3

Simplifique os termos.

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Etapa 3.1

Simplifique cada termo.

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Etapa 3.1.1

Avalie $\cos (- 1)$ .

$(\sin (x) \cdot 0.5403023 - \cos (x) \sin (- 1)) \sin (x - 1)$

Etapa 3.1.2

Mova $0.5403023$ para a esquerda de $\sin (x)$ .

$(0.5403023 \cdot \sin (x) - \cos (x) \sin (- 1)) \sin (x - 1)$

Etapa 3.1.3

Avalie $\sin (- 1)$ .

$(0.5403023 \sin (x) - \cos (x) \cdot - 0.84147098) \sin (x - 1)$

Etapa 3.1.4

Multiplique $- 0.84147098$ por $- 1$ .

$(0.5403023 \sin (x) + 0.84147098 \cos (x)) \sin (x - 1)$

Etapa 3.2

Separar negativação.

$(0.5403023 \sin (x) + 0.84147098 \cos (x)) \sin (x - (1))$

Etapa 4

Aplique a fórmula da diferença dos ângulos.

$(0.5403023 \sin (x) + 0.84147098 \cos (x)) (\sin (x) \cos (1) - \cos (x) \sin (1))$

Etapa 5

Simplifique cada termo.

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Etapa 5.1

Avalie $\cos (1)$ .

$(0.5403023 \sin (x) + 0.84147098 \cos (x)) (\sin (x) \cdot 0.5403023 - \cos (x) \sin (1))$

Etapa 5.2

Mova $0.5403023$ para a esquerda de $\sin (x)$ .

$(0.5403023 \sin (x) + 0.84147098 \cos (x)) (0.5403023 \cdot \sin (x) - \cos (x) \sin (1))$

Etapa 5.3

Avalie $\sin (1)$ .

$(0.5403023 \sin (x) + 0.84147098 \cos (x)) (0.5403023 \sin (x) - \cos (x) \cdot 0.84147098)$

Etapa 5.4

Multiplique $0.84147098$ por $- 1$ .

$(0.5403023 \sin (x) + 0.84147098 \cos (x)) (0.5403023 \sin (x) - 0.84147098 \cos (x))$

Etapa 6

Expanda $(0.5403023 \sin (x) + 0.84147098 \cos (x)) (0.5403023 \sin (x) - 0.84147098 \cos (x))$ usando o método FOIL.

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Etapa 6.1

Aplique a propriedade distributiva.

$0.5403023 \sin (x) (0.5403023 \sin (x) - 0.84147098 \cos (x)) + 0.84147098 \cos (x) (0.5403023 \sin (x) - 0.84147098 \cos (x))$

Etapa 6.2

Aplique a propriedade distributiva.

$0.5403023 \sin (x) (0.5403023 \sin (x)) + 0.5403023 \sin (x) (- 0.84147098 \cos (x)) + 0.84147098 \cos (x) (0.5403023 \sin (x) - 0.84147098 \cos (x))$

Etapa 6.3

Aplique a propriedade distributiva.

$0.5403023 \sin (x) (0.5403023 \sin (x)) + 0.5403023 \sin (x) (- 0.84147098 \cos (x)) + 0.84147098 \cos (x) (0.5403023 \sin (x)) + 0.84147098 \cos (x) (- 0.84147098 \cos (x))$

Etapa 7

Simplifique e combine termos semelhantes.

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Etapa 7.1

Simplifique cada termo.

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Etapa 7.1.1

Multiplique $0.5403023 \sin (x) (0.5403023 \sin (x))$ .

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Etapa 7.1.1.1

Multiplique $0.5403023$ por $0.5403023$ .

$0.29192658 \sin (x) \sin (x) + 0.5403023 \sin (x) (- 0.84147098 \cos (x)) + 0.84147098 \cos (x) (0.5403023 \sin (x)) + 0.84147098 \cos (x) (- 0.84147098 \cos (x))$

Etapa 7.1.1.2

Eleve $\sin (x)$ à potência de $1$ .

$0.29192658 (\sin^{1} (x) \sin (x)) + 0.5403023 \sin (x) (- 0.84147098 \cos (x)) + 0.84147098 \cos (x) (0.5403023 \sin (x)) + 0.84147098 \cos (x) (- 0.84147098 \cos (x))$

Etapa 7.1.1.3

Eleve $\sin (x)$ à potência de $1$ .

$0.29192658 (\sin^{1} (x) \sin^{1} (x)) + 0.5403023 \sin (x) (- 0.84147098 \cos (x)) + 0.84147098 \cos (x) (0.5403023 \sin (x)) + 0.84147098 \cos (x) (- 0.84147098 \cos (x))$

Etapa 7.1.1.4

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$0.29192658 {\sin (x)}^{1 + 1} + 0.5403023 \sin (x) (- 0.84147098 \cos (x)) + 0.84147098 \cos (x) (0.5403023 \sin (x)) + 0.84147098 \cos (x) (- 0.84147098 \cos (x))$

Etapa 7.1.1.5

Some $1$ e $1$ .

$0.29192658 \sin^{2} (x) + 0.5403023 \sin (x) (- 0.84147098 \cos (x)) + 0.84147098 \cos (x) (0.5403023 \sin (x)) + 0.84147098 \cos (x) (- 0.84147098 \cos (x))$

Etapa 7.1.2

Multiplique $- 0.84147098$ por $0.5403023$ .

$0.29192658 \sin^{2} (x) - 0.45464871 \sin (x) \cos (x) + 0.84147098 \cos (x) (0.5403023 \sin (x)) + 0.84147098 \cos (x) (- 0.84147098 \cos (x))$

Etapa 7.1.3

Multiplique $0.5403023$ por $0.84147098$ .

$0.29192658 \sin^{2} (x) - 0.45464871 \sin (x) \cos (x) + 0.45464871 \cos (x) \sin (x) + 0.84147098 \cos (x) (- 0.84147098 \cos (x))$

Etapa 7.1.4

Multiplique $0.84147098 \cos (x) (- 0.84147098 \cos (x))$ .

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Etapa 7.1.4.1

Multiplique $- 0.84147098$ por $0.84147098$ .

$0.29192658 \sin^{2} (x) - 0.45464871 \sin (x) \cos (x) + 0.45464871 \cos (x) \sin (x) - 0.70807341 \cos (x) \cos (x)$

Etapa 7.1.4.2

Eleve $\cos (x)$ à potência de $1$ .

$0.29192658 \sin^{2} (x) - 0.45464871 \sin (x) \cos (x) + 0.45464871 \cos (x) \sin (x) - 0.70807341 (\cos^{1} (x) \cos (x))$

Etapa 7.1.4.3

Eleve $\cos (x)$ à potência de $1$ .

$0.29192658 \sin^{2} (x) - 0.45464871 \sin (x) \cos (x) + 0.45464871 \cos (x) \sin (x) - 0.70807341 (\cos^{1} (x) \cos^{1} (x))$

Etapa 7.1.4.4

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$0.29192658 \sin^{2} (x) - 0.45464871 \sin (x) \cos (x) + 0.45464871 \cos (x) \sin (x) - 0.70807341 {\cos (x)}^{1 + 1}$

Etapa 7.1.4.5

Some $1$ e $1$ .

$0.29192658 \sin^{2} (x) - 0.45464871 \sin (x) \cos (x) + 0.45464871 \cos (x) \sin (x) - 0.70807341 \cos^{2} (x)$

Etapa 7.2

Reordene os fatores de $- 0.45464871 \sin (x) \cos (x)$ .

$0.29192658 \sin^{2} (x) - 0.45464871 \cos (x) \sin (x) + 0.45464871 \cos (x) \sin (x) - 0.70807341 \cos^{2} (x)$

Etapa 7.3

Some $- 0.45464871 \cos (x) \sin (x)$ e $0.45464871 \cos (x) \sin (x)$ .

$0.29192658 \sin^{2} (x) + 0 \cos (x) \sin (x) - 0.70807341 \cos^{2} (x)$

Etapa 8

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Etapa 8.1

Multiplique $0$ por $\cos (x)$ .

$0.29192658 \sin^{2} (x) + 0 \sin (x) - 0.70807341 \cos^{2} (x)$

Etapa 8.2

Multiplique $0$ por $\sin (x)$ .

$0.29192658 \sin^{2} (x) + 0 - 0.70807341 \cos^{2} (x)$

Etapa 9

Some $0.29192658 \sin^{2} (x)$ e $0$ .

$0.29192658 \sin^{2} (x) - 0.70807341 \cos^{2} (x)$