Trigonometry Examples

$v (({(- \frac{1}{5})}^{2}) + {(\frac{1}{2})}^{2})$

Step 1

Simplify each term.

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Step 1.1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1.1

Apply the product rule to $- \frac{1}{5}$ .

$v ({(- 1)}^{2} {(\frac{1}{5})}^{2} + {(\frac{1}{2})}^{2})$

Step 1.1.2

Apply the product rule to $\frac{1}{5}$ .

$v ({(- 1)}^{2} \frac{1^{2}}{5^{2}} + {(\frac{1}{2})}^{2})$

Step 1.2

Raise $- 1$ to the power of $2$ .

$v (1 \frac{1^{2}}{5^{2}} + {(\frac{1}{2})}^{2})$

Step 1.3

Multiply $\frac{1^{2}}{5^{2}}$ by $1$ .

$v (\frac{1^{2}}{5^{2}} + {(\frac{1}{2})}^{2})$

Step 1.4

One to any power is one.

$v (\frac{1}{5^{2}} + {(\frac{1}{2})}^{2})$

Step 1.5

Raise $5$ to the power of $2$ .

$v (\frac{1}{25} + {(\frac{1}{2})}^{2})$

Step 1.6

Apply the product rule to $\frac{1}{2}$ .

$v (\frac{1}{25} + \frac{1^{2}}{2^{2}})$

Step 1.7

One to any power is one.

$v (\frac{1}{25} + \frac{1}{2^{2}})$

Step 1.8

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

$v (\frac{1}{25} + \frac{1}{4})$

Step 2

To write $\frac{1}{25}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$v (\frac{1}{25} \cdot \frac{4}{4} + \frac{1}{4})$

Step 3

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{25}{25}$ .

$v (\frac{1}{25} \cdot \frac{4}{4} + \frac{1}{4} \cdot \frac{25}{25})$

Step 4

Write each expression with a common denominator of $100$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{1}{25}$ by $\frac{4}{4}$ .

$v (\frac{4}{25 \cdot 4} + \frac{1}{4} \cdot \frac{25}{25})$

Step 4.2

Multiply $25$ by $4$ .

$v (\frac{4}{100} + \frac{1}{4} \cdot \frac{25}{25})$

Step 4.3

Multiply $\frac{1}{4}$ by $\frac{25}{25}$ .

$v (\frac{4}{100} + \frac{25}{4 \cdot 25})$

Step 4.4

Multiply $4$ by $25$ .

$v (\frac{4}{100} + \frac{25}{100})$

Step 5

Simplify the expression.

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Step 5.1

Combine the numerators over the common denominator.

$v \frac{4 + 25}{100}$

Step 5.2

Add $4$ and $25$ .

$v \frac{29}{100}$

Step 6

Combine $v$ and $\frac{29}{100}$ .

$\frac{v \cdot 29}{100}$

Step 7

Move $29$ to the left of $v$ .

$\frac{29 v}{100}$