Pré-cálculo Exemplos

$20 \sum_{x = 0}^{3} | \sin (2.8 π x) \cdot \sin (3.48 π x) |$

Etapa 1

Simplifique a soma.

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Etapa 1.1

Multiplique $2.8$ por $π$ .

$| \sin (8.79645943 x) \cdot \sin (3.48 π x) |$

Etapa 1.2

Multiplique $3.48$ por $π$ .

$| \sin (8.79645943 x) \sin (10.93274243 x) |$

Etapa 1.3

Reescreva a soma.

$20 \sum_{x = 0}^{3} | \sin (8.79645943 x) \sin (10.93274243 x) |$

Etapa 2

Expanda a série para cada valor de $x$ .

$20 (| \sin (8.79645943 \cdot 0) \sin (10.93274243 \cdot 0) | + | \sin (8.79645943 \cdot 1) \sin (10.93274243 \cdot 1) | + | \sin (8.79645943 \cdot 2) \sin (10.93274243 \cdot 2) | + | \sin (8.79645943 \cdot 3) \sin (10.93274243 \cdot 3) |)$

Etapa 3

Simplifique.

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Etapa 3.1

Avalie $\sin (8.79645943 \cdot 0)$ .

$20 (| 0 \sin (10.93274243 \cdot 0) | + | \sin (8.79645943 \cdot 1) \sin (10.93274243 \cdot 1) | + | \sin (8.79645943 \cdot 2) \sin (10.93274243 \cdot 2) | + | \sin (8.79645943 \cdot 3) \sin (10.93274243 \cdot 3) |)$

Etapa 3.2

Avalie $\sin (10.93274243 \cdot 0)$ .

$20 (| 0 \cdot 0 | + | \sin (8.79645943 \cdot 1) \sin (10.93274243 \cdot 1) | + | \sin (8.79645943 \cdot 2) \sin (10.93274243 \cdot 2) | + | \sin (8.79645943 \cdot 3) \sin (10.93274243 \cdot 3) |)$

Etapa 3.3

Multiplique $0$ por $0$ .

$20 (| 0 | + | \sin (8.79645943 \cdot 1) \sin (10.93274243 \cdot 1) | + | \sin (8.79645943 \cdot 2) \sin (10.93274243 \cdot 2) | + | \sin (8.79645943 \cdot 3) \sin (10.93274243 \cdot 3) |)$

Etapa 3.4

O valor absoluto é a distância entre um número e zero. A distância entre $0$ e $0$ é $0$ .

$20 (0 + | \sin (8.79645943 \cdot 1) \sin (10.93274243 \cdot 1) | + | \sin (8.79645943 \cdot 2) \sin (10.93274243 \cdot 2) | + | \sin (8.79645943 \cdot 3) \sin (10.93274243 \cdot 3) |)$

Etapa 3.5

Avalie $\sin (8.79645943 \cdot 1)$ .

$20 (0 + | 0.58778525 \sin (10.93274243 \cdot 1) | + | \sin (8.79645943 \cdot 2) \sin (10.93274243 \cdot 2) | + | \sin (8.79645943 \cdot 3) \sin (10.93274243 \cdot 3) |)$

Etapa 3.6

Avalie $\sin (10.93274243 \cdot 1)$ .

$20 (0 + | 0.58778525 \cdot 0.18965656 | + | \sin (8.79645943 \cdot 2) \sin (10.93274243 \cdot 2) | + | \sin (8.79645943 \cdot 3) \sin (10.93274243 \cdot 3) |)$

Etapa 3.7

Multiplique $0.58778525$ por $0.18965656$ .

$20 (0 + | 0.11147733 | + | \sin (8.79645943 \cdot 2) \sin (10.93274243 \cdot 2) | + | \sin (8.79645943 \cdot 3) \sin (10.93274243 \cdot 3) |)$

Etapa 3.8

O valor absoluto é a distância entre um número e zero. A distância entre $0$ e $0.11147733$ é $0.11147733$ .

$20 (0 + 0.11147733 + | \sin (8.79645943 \cdot 2) \sin (10.93274243 \cdot 2) | + | \sin (8.79645943 \cdot 3) \sin (10.93274243 \cdot 3) |)$

Etapa 3.9

Some $0$ e $0.11147733$ .

$20 (0.11147733 + | \sin (8.79645943 \cdot 2) \sin (10.93274243 \cdot 2) | + | \sin (8.79645943 \cdot 3) \sin (10.93274243 \cdot 3) |)$

Etapa 3.10

Avalie $\sin (8.79645943 \cdot 2)$ .

$20 (0.11147733 + | 0.30225208 \sin (10.93274243 \cdot 2) | + | \sin (8.79645943 \cdot 3) \sin (10.93274243 \cdot 3) |)$

Etapa 3.11

Avalie $\sin (10.93274243 \cdot 2)$ .

$20 (0.11147733 + | 0.30225208 \cdot 0.37242878 | + | \sin (8.79645943 \cdot 3) \sin (10.93274243 \cdot 3) |)$

Etapa 3.12

Multiplique $0.30225208$ por $0.37242878$ .

$20 (0.11147733 + | 0.11256737 | + | \sin (8.79645943 \cdot 3) \sin (10.93274243 \cdot 3) |)$

Etapa 3.13

O valor absoluto é a distância entre um número e zero. A distância entre $0$ e $0.11256737$ é $0.11256737$ .

$20 (0.11147733 + 0.11256737 + | \sin (8.79645943 \cdot 3) \sin (10.93274243 \cdot 3) |)$

Etapa 3.14

Some $0.11147733$ e $0.11256737$ .

$20 (0.2240447 + | \sin (8.79645943 \cdot 3) \sin (10.93274243 \cdot 3) |)$

Etapa 3.15

Avalie $\sin (8.79645943 \cdot 3)$ .

$20 (0.2240447 + | 0.44446912 \sin (10.93274243 \cdot 3) |)$

Etapa 3.16

Avalie $\sin (10.93274243 \cdot 3)$ .

$20 (0.2240447 + | 0.44446912 \cdot 0.5416822 |)$

Etapa 3.17

Multiplique $0.44446912$ por $0.5416822$ .

$20 (0.2240447 + | 0.24076101 |)$

Etapa 3.18

O valor absoluto é a distância entre um número e zero. A distância entre $0$ e $0.24076101$ é $0.24076101$ .

$20 (0.2240447 + 0.24076101)$

Etapa 3.19

Some $0.2240447$ e $0.24076101$ .

$20 \cdot 0.46480572$

Etapa 3.20

Multiplique $20$ por $0.46480572$ .

$9.29611442$