Trigonometría Ejemplos

f (4) = - 5 x \sin^{2} (x) + 5 x \cos^{2} (x) + 5 \cos (x) \sin (x)

$f (4) = - 5 x \sin^{2} (x) + 5 x \cos^{2} (x) + 5 \cos (x) \sin (x)$

Paso 1

Reemplaza la variable

x

$x$ con

4

$4$ en la expresión.

f (4) = - 5 \cdot 4 \sin^{2} (4) + 5 (4) \cos^{2} (4) + 5 \cos (4) \sin (4)

$f (4) = - 5 \cdot 4 \sin^{2} (4) + 5 (4) \cos^{2} (4) + 5 \cos (4) \sin (4)$

Paso 2

Simplifica el resultado.

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Paso 2.1

Simplifica cada término.

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Paso 2.1.1

Multiplica

- 5

$- 5$ por

4

$4$ .

f (4) = - 20 \sin^{2} (4) + 5 (4) \cos^{2} (4) + 5 \cos (4) \sin (4)

$f (4) = - 20 \sin^{2} (4) + 5 (4) \cos^{2} (4) + 5 \cos (4) \sin (4)$

Paso 2.1.2

Evalúa

\sin (4)

$\sin (4)$ .

f (4) = - 20 \cdot {0.06975647}^{2} + 5 (4) \cos^{2} (4) + 5 \cos (4) \sin (4)

$f (4) = - 20 \cdot {0.06975647}^{2} + 5 (4) \cos^{2} (4) + 5 \cos (4) \sin (4)$

Paso 2.1.3

Eleva

0.06975647

$0.06975647$ a la potencia de

2

$2$ .

f (4) = - 20 \cdot 0.00486596 + 5 (4) \cos^{2} (4) + 5 \cos (4) \sin (4)

$f (4) = - 20 \cdot 0.00486596 + 5 (4) \cos^{2} (4) + 5 \cos (4) \sin (4)$

Paso 2.1.4

Multiplica

- 20

$- 20$ por

0.00486596

$0.00486596$ .

f (4) = - 0.09731931 + 5 (4) \cos^{2} (4) + 5 \cos (4) \sin (4)

$f (4) = - 0.09731931 + 5 (4) \cos^{2} (4) + 5 \cos (4) \sin (4)$

Paso 2.1.5

Multiplica

5

$5$ por

4

$4$ .

f (4) = - 0.09731931 + 20 \cos^{2} (4) + 5 \cos (4) \sin (4)

$f (4) = - 0.09731931 + 20 \cos^{2} (4) + 5 \cos (4) \sin (4)$

Paso 2.1.6

Evalúa

\cos (4)

$\cos (4)$ .

f (4) = - 0.09731931 + 20 \cdot {0.99756405}^{2} + 5 \cos (4) \sin (4)

$f (4) = - 0.09731931 + 20 \cdot {0.99756405}^{2} + 5 \cos (4) \sin (4)$

Paso 2.1.7

Eleva

0.99756405

$0.99756405$ a la potencia de

2

$2$ .

f (4) = - 0.09731931 + 20 \cdot 0.99513403 + 5 \cos (4) \sin (4)

$f (4) = - 0.09731931 + 20 \cdot 0.99513403 + 5 \cos (4) \sin (4)$

Paso 2.1.8

Multiplica

20

$20$ por

0.99513403

$0.99513403$ .

f (4) = - 0.09731931 + 19.90268068 + 5 \cos (4) \sin (4)

$f (4) = - 0.09731931 + 19.90268068 + 5 \cos (4) \sin (4)$

Paso 2.1.9

Evalúa

\cos (4)

$\cos (4)$ .

f (4) = - 0.09731931 + 19.90268068 + 5 \cdot (0.99756405 \sin (4))

$f (4) = - 0.09731931 + 19.90268068 + 5 \cdot (0.99756405 \sin (4))$

Paso 2.1.10

Multiplica

5

$5$ por

0.99756405

$0.99756405$ .

f (4) = - 0.09731931 + 19.90268068 + 4.98782025 \sin (4)

$f (4) = - 0.09731931 + 19.90268068 + 4.98782025 \sin (4)$

Paso 2.1.11

Evalúa

\sin (4)

$\sin (4)$ .

f (4) = - 0.09731931 + 19.90268068 + 4.98782025 \cdot 0.06975647

$f (4) = - 0.09731931 + 19.90268068 + 4.98782025 \cdot 0.06975647$

Paso 2.1.12

Multiplica

4.98782025

$4.98782025$ por

0.06975647

$0.06975647$ .

f (4) = - 0.09731931 + 19.90268068 + 0.34793275

$f (4) = - 0.09731931 + 19.90268068 + 0.34793275$

f (4) = - 0.09731931 + 19.90268068 + 0.34793275

$f (4) = - 0.09731931 + 19.90268068 + 0.34793275$

Paso 2.2

Simplifica mediante la adición de números.

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Paso 2.2.1

Suma

- 0.09731931

$- 0.09731931$ y

19.90268068

$19.90268068$ .

f (4) = 19.80536137 + 0.34793275

$f (4) = 19.80536137 + 0.34793275$

Paso 2.2.2

Suma

19.80536137

$19.80536137$ y

0.34793275

$0.34793275$ .

f (4) = 20.15329412

$f (4) = 20.15329412$

f (4) = 20.15329412

$f (4) = 20.15329412$

Paso 2.3

La respuesta final es

20.15329412

$20.15329412$ .

20.15329412

$20.15329412$

20.15329412

$20.15329412$

Paso 3