Trigonometry Examples

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

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

Step 1

Replace the variable

x

$x$ with

4

$4$ in the expression.

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

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

Step 2

Simplify the result.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply

- 5

$- 5$ by

4

$4$ .

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

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

Step 2.1.2

Evaluate

\sin (4)

$\sin (4)$ .

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

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

Step 2.1.3

Raise

0.06975647

$0.06975647$ to the power of

2

$2$ .

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

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

Step 2.1.4

Multiply

- 20

$- 20$ by

0.00486596

$0.00486596$ .

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

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

Step 2.1.5

Multiply

5

$5$ by

4

$4$ .

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

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

Step 2.1.6

Evaluate

\cos (4)

$\cos (4)$ .

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

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

Step 2.1.7

Raise

0.99756405

$0.99756405$ to the power of

2

$2$ .

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

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

Step 2.1.8

Multiply

20

$20$ by

0.99513403

$0.99513403$ .

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

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

Step 2.1.9

Evaluate

\cos (4)

$\cos (4)$ .

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

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

Step 2.1.10

Multiply

5

$5$ by

0.99756405

$0.99756405$ .

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

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

Step 2.1.11

Evaluate

\sin (4)

$\sin (4)$ .

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

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

Step 2.1.12

Multiply

4.98782025

$4.98782025$ by

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

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

Step 2.2

Simplify by adding numbers.

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Step 2.2.1

Add

- 0.09731931

$- 0.09731931$ and

19.90268068

$19.90268068$ .

f (4) = 19.80536137 + 0.34793275

$f (4) = 19.80536137 + 0.34793275$

Step 2.2.2

Add

19.80536137

$19.80536137$ and

0.34793275

$0.34793275$ .

f (4) = 20.15329412

$f (4) = 20.15329412$

f (4) = 20.15329412

$f (4) = 20.15329412$

Step 2.3

The final answer is

20.15329412

$20.15329412$ .

20.15329412

$20.15329412$

20.15329412

$20.15329412$

Step 3