Pré-cálculo Exemplos

$\cos (x) - \sin^{2} (x - 1)$

Etapa 1

Separar negativação.

$\cos (x) - \sin^{2} (x - (1))$

Etapa 2

Aplique a fórmula da diferença dos ângulos.

$\cos (x) - {(\sin (x) \cos (1) - \cos (x) \sin (1))}^{2}$

Etapa 3

Simplifique cada termo.

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Etapa 3.1

Avalie $\cos (1)$ .

$\cos (x) - {(\sin (x) \cdot 0.5403023 - \cos (x) \sin (1))}^{2}$

Etapa 3.2

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

$\cos (x) - {(0.5403023 \cdot \sin (x) - \cos (x) \sin (1))}^{2}$

Etapa 3.3

Avalie $\sin (1)$ .

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

Etapa 3.4

Multiplique $0.84147098$ por $- 1$ .

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

Etapa 4

Reescreva ${(0.5403023 \sin (x) - 0.84147098 \cos (x))}^{2}$ como $(0.5403023 \sin (x) - 0.84147098 \cos (x)) (0.5403023 \sin (x) - 0.84147098 \cos (x))$ .

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

Etapa 5

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 5.1

Aplique a propriedade distributiva.

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

Etapa 5.2

Aplique a propriedade distributiva.

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

Etapa 5.3

Aplique a propriedade distributiva.

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

Etapa 6

Simplifique e combine termos semelhantes.

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Etapa 6.1

Simplifique cada termo.

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Etapa 6.1.1

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

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Etapa 6.1.1.1

Multiplique $0.5403023$ por $0.5403023$ .

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

Etapa 6.1.1.2

Eleve $\sin (x)$ à potência de $1$ .

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

Etapa 6.1.1.3

Eleve $\sin (x)$ à potência de $1$ .

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

Etapa 6.1.1.4

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

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

Etapa 6.1.1.5

Some $1$ e $1$ .

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

Etapa 6.1.2

Multiplique $- 0.84147098$ por $0.5403023$ .

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

Etapa 6.1.3

Multiplique $0.5403023$ por $- 0.84147098$ .

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

Etapa 6.1.4

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

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Etapa 6.1.4.1

Multiplique $- 0.84147098$ por $- 0.84147098$ .

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

Etapa 6.1.4.2

Eleve $\cos (x)$ à potência de $1$ .

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

Etapa 6.1.4.3

Eleve $\cos (x)$ à potência de $1$ .

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

Etapa 6.1.4.4

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

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

Etapa 6.1.4.5

Some $1$ e $1$ .

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

Etapa 6.2

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

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

Etapa 6.3

Subtraia $0.45464871 \cos (x) \sin (x)$ de $- 0.45464871 \cos (x) \sin (x)$ .

$\cos (x) - (0.29192658 \sin^{2} (x) - 0.90929742 \cos (x) \sin (x) + 0.70807341 \cos^{2} (x))$

Etapa 7

Aplique a propriedade distributiva.

$\cos (x) - (0.29192658 \sin^{2} (x)) - (- 0.90929742 \cos (x) \sin (x)) - (0.70807341 \cos^{2} (x))$

Etapa 8

Simplifique.

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Etapa 8.1

Multiplique $0.29192658$ por $- 1$ .

$\cos (x) - 0.29192658 \sin^{2} (x) - (- 0.90929742 \cos (x) \sin (x)) - (0.70807341 \cos^{2} (x))$

Etapa 8.2

Multiplique $- 0.90929742$ por $- 1$ .

$\cos (x) - 0.29192658 \sin^{2} (x) + 0.90929742 (\cos (x) \sin (x)) - (0.70807341 \cos^{2} (x))$

Etapa 8.3

Multiplique $0.70807341$ por $- 1$ .

$\cos (x) - 0.29192658 \sin^{2} (x) + 0.90929742 (\cos (x) \sin (x)) - 0.70807341 \cos^{2} (x)$

$\cos (x) - 0.29192658 \sin^{2} (x) + 0.90929742 \cos (x) \sin (x) - 0.70807341 \cos^{2} (x)$