Trigonometry Examples

$v ((\frac{3}{10} \cdot 4) - (\frac{3}{10})) (\frac{3}{10})$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $2$ .

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Step 1.1.1

Factor $2$ out of $10$ .

$v (\frac{3}{2 (5)} \cdot 4 - (\frac{3}{10})) \frac{3}{10}$

Step 1.1.2

Factor $2$ out of $4$ .

$v (\frac{3}{2 \cdot 5} \cdot (2 \cdot 2) - (\frac{3}{10})) \frac{3}{10}$

Step 1.1.3

Cancel the common factor.

$v (\frac{3}{2 \cdot 5} \cdot (2 \cdot 2) - (\frac{3}{10})) \frac{3}{10}$

Step 1.1.4

Rewrite the expression.

$v (\frac{3}{5} \cdot 2 - (\frac{3}{10})) \frac{3}{10}$

Step 1.2

Combine $\frac{3}{5}$ and $2$ .

$v (\frac{3 \cdot 2}{5} - (\frac{3}{10})) \frac{3}{10}$

Step 1.3

Multiply $3$ by $2$ .

$v (\frac{6}{5} - \frac{3}{10}) \frac{3}{10}$

Step 2

To write $\frac{6}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$v (\frac{6}{5} \cdot \frac{2}{2} - \frac{3}{10}) \frac{3}{10}$

Step 3

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{6}{5}$ by $\frac{2}{2}$ .

$v (\frac{6 \cdot 2}{5 \cdot 2} - \frac{3}{10}) \frac{3}{10}$

Step 3.2

Multiply $5$ by $2$ .

$v (\frac{6 \cdot 2}{10} - \frac{3}{10}) \frac{3}{10}$

Step 4

Combine the numerators over the common denominator.

$v \frac{6 \cdot 2 - 3}{10} \frac{3}{10}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $6$ by $2$ .

$v \frac{12 - 3}{10} \frac{3}{10}$

Step 5.2

Subtract $3$ from $12$ .

$v \frac{9}{10} \frac{3}{10}$

Step 6

Combine $v$ and $\frac{9}{10}$ .

$\frac{v \cdot 9}{10} \cdot \frac{3}{10}$

Step 7

Move $9$ to the left of $v$ .

$\frac{9 \cdot v}{10} \cdot \frac{3}{10}$

Step 8

Multiply $\frac{9 v}{10} \cdot \frac{3}{10}$ .

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Step 8.1

Multiply $\frac{9 v}{10}$ by $\frac{3}{10}$ .

$\frac{9 v \cdot 3}{10 \cdot 10}$

Step 8.2

Multiply $3$ by $9$ .

$\frac{27 v}{10 \cdot 10}$

Step 8.3

Multiply $10$ by $10$ .

$\frac{27 v}{100}$