Trigonometry Examples

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

Step 1

Replace the variable $x$ with $4$ in the expression.

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

Step 2

Simplify the result.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $- 5$ by $4$ .

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

Step 2.1.2

Evaluate $\sin (4)$ .

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

Step 2.1.3

Raise $0.06975647$ to the power of $2$ .

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

Step 2.1.4

Multiply $- 20$ by $0.00486596$ .

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

Step 2.1.5

Multiply $5$ by $4$ .

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

Step 2.1.6

Evaluate $\cos (4)$ .

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

Step 2.1.7

Raise $0.99756405$ to the power of $2$ .

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

Step 2.1.8

Multiply $20$ by $0.99513403$ .

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

Step 2.1.9

Evaluate $\cos (4)$ .

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

Step 2.1.10

Multiply $5$ by $0.99756405$ .

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

Step 2.1.11

Evaluate $\sin (4)$ .

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

Step 2.1.12

Multiply $4.98782025$ by $0.06975647$ .

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

Step 2.2

Simplify by adding numbers.

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Step 2.2.1

Add $- 0.09731931$ and $19.90268068$ .

$f (4) = 19.80536137 + 0.34793275$

Step 2.2.2

Add $19.80536137$ and $0.34793275$ .

$f (4) = 20.15329412$

Step 2.3

The final answer is $20.15329412$ .

$20.15329412$

Step 3