Trigonometry Examples

$\frac{3}{10} \cdot (- 3 e^{- 3 \cdot 0.2} + \sin (0.2) + 3 \cos (0.2))$

Step 1

Simplify each term.

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Step 1.1

Multiply $- 3$ by $0.2$ .

$\frac{3}{10} \cdot (- 3 e^{- 0.6} + \sin (0.2) + 3 \cos (0.2))$

Step 1.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{3}{10} \cdot (- 3 \frac{1}{e^{0.6}} + \sin (0.2) + 3 \cos (0.2))$

Step 1.3

Combine $- 3$ and $\frac{1}{e^{0.6}}$ .

$\frac{3}{10} \cdot (\frac{- 3}{e^{0.6}} + \sin (0.2) + 3 \cos (0.2))$

Step 1.4

Move the negative in front of the fraction.

$\frac{3}{10} \cdot (- \frac{3}{e^{0.6}} + \sin (0.2) + 3 \cos (0.2))$

Step 2

Apply the distributive property.

$\frac{3}{10} (- \frac{3}{e^{0.6}}) + \frac{3}{10} \sin (0.2) + \frac{3}{10} (3 \cos (0.2))$

Step 3

Simplify.

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Step 3.1

Multiply $\frac{3}{10} (- \frac{3}{e^{0.6}})$ .

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Step 3.1.1

Multiply $\frac{3}{10}$ by $\frac{3}{e^{0.6}}$ .

$- \frac{3 \cdot 3}{10 e^{0.6}} + \frac{3}{10} \sin (0.2) + \frac{3}{10} (3 \cos (0.2))$

Step 3.1.2

Multiply $3$ by $3$ .

$- \frac{9}{10 e^{0.6}} + \frac{3}{10} \sin (0.2) + \frac{3}{10} (3 \cos (0.2))$

Step 3.2

Combine $\frac{3}{10}$ and $\sin (0.2)$ .

$- \frac{9}{10 e^{0.6}} + \frac{3 \sin (0.2)}{10} + \frac{3}{10} (3 \cos (0.2))$

Step 3.3

Multiply $\frac{3}{10} (3 \cos (0.2))$ .

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Step 3.3.1

Combine $3$ and $\frac{3}{10}$ .

$- \frac{9}{10 e^{0.6}} + \frac{3 \sin (0.2)}{10} + \frac{3 \cdot 3}{10} \cos (0.2)$

Step 3.3.2

Multiply $3$ by $3$ .

$- \frac{9}{10 e^{0.6}} + \frac{3 \sin (0.2)}{10} + \frac{9}{10} \cos (0.2)$

Step 3.3.3

Combine $\frac{9}{10}$ and $\cos (0.2)$ .

$- \frac{9}{10 e^{0.6}} + \frac{3 \sin (0.2)}{10} + \frac{9 \cos (0.2)}{10}$

Step 4

Simplify each term.

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Step 4.1

Evaluate $\sin (0.2)$ .

$- \frac{9}{10 e^{0.6}} + \frac{3 \cdot 0.19866933}{10} + \frac{9 \cos (0.2)}{10}$

Step 4.2

Multiply $3$ by $0.19866933$ .

$- \frac{9}{10 e^{0.6}} + \frac{0.59600799}{10} + \frac{9 \cos (0.2)}{10}$

Step 4.3

Divide $0.59600799$ by $10$ .

$- \frac{9}{10 e^{0.6}} + 0.05960079 + \frac{9 \cos (0.2)}{10}$

Step 4.4

Evaluate $\cos (0.2)$ .

$- \frac{9}{10 e^{0.6}} + 0.05960079 + \frac{9 \cdot 0.98006657}{10}$

Step 4.5

Multiply $9$ by $0.98006657$ .

$- \frac{9}{10 e^{0.6}} + 0.05960079 + \frac{8.8205992}{10}$

Step 4.6

Divide $8.8205992$ by $10$ .

$- \frac{9}{10 e^{0.6}} + 0.05960079 + 0.88205992$

Step 5

Simplify by adding terms.

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Step 5.1

Add $- \frac{9}{10 e^{0.6}}$ and $0.05960079$ .

$- 0.43432967 + 0.88205992$

Step 5.2

Add $- 0.43432967$ and $0.88205992$ .

$0.44773024$