Trigonometry Examples

$2 (- \frac{1}{\sqrt{10}}) (\frac{5}{\sqrt{10}})$

Step 1

Multiply $\frac{1}{\sqrt{10}}$ by $\frac{\sqrt{10}}{\sqrt{10}}$ .

$2 (- (\frac{1}{\sqrt{10}} \cdot \frac{\sqrt{10}}{\sqrt{10}})) \cdot \frac{5}{\sqrt{10}}$

Step 2

Combine and simplify the denominator.

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Step 2.1

Multiply $\frac{1}{\sqrt{10}}$ by $\frac{\sqrt{10}}{\sqrt{10}}$ .

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

Step 2.2

Raise $\sqrt{10}$ to the power of $1$ .

$2 (- \frac{\sqrt{10}}{{\sqrt{10}}^{1} \sqrt{10}}) \cdot \frac{5}{\sqrt{10}}$

Step 2.3

Raise $\sqrt{10}$ to the power of $1$ .

$2 (- \frac{\sqrt{10}}{{\sqrt{10}}^{1} {\sqrt{10}}^{1}}) \cdot \frac{5}{\sqrt{10}}$

Step 2.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 (- \frac{\sqrt{10}}{{\sqrt{10}}^{1 + 1}}) \cdot \frac{5}{\sqrt{10}}$

Step 2.5

Add $1$ and $1$ .

$2 (- \frac{\sqrt{10}}{{\sqrt{10}}^{2}}) \cdot \frac{5}{\sqrt{10}}$

Step 2.6

Rewrite ${\sqrt{10}}^{2}$ as $10$ .

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Step 2.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10}$ as $10^{\frac{1}{2}}$ .

$2 (- \frac{\sqrt{10}}{{(10^{\frac{1}{2}})}^{2}}) \cdot \frac{5}{\sqrt{10}}$

Step 2.6.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2 (- \frac{\sqrt{10}}{10^{\frac{1}{2} \cdot 2}}) \cdot \frac{5}{\sqrt{10}}$

Step 2.6.3

Combine $\frac{1}{2}$ and $2$ .

$2 (- \frac{\sqrt{10}}{10^{\frac{2}{2}}}) \cdot \frac{5}{\sqrt{10}}$

Step 2.6.4

Cancel the common factor of $2$ .

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Step 2.6.4.1

Cancel the common factor.

$2 (- \frac{\sqrt{10}}{10^{\frac{2}{2}}}) \cdot \frac{5}{\sqrt{10}}$

Step 2.6.4.2

Rewrite the expression.

$2 (- \frac{\sqrt{10}}{10^{1}}) \cdot \frac{5}{\sqrt{10}}$

Step 2.6.5

Evaluate the exponent.

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

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Move the leading negative in $- \frac{\sqrt{10}}{10}$ into the numerator.

$2 \frac{- \sqrt{10}}{10} \cdot \frac{5}{\sqrt{10}}$

Step 3.2

Factor $2$ out of $10$ .

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

Step 3.3

Cancel the common factor.

$2 \frac{- \sqrt{10}}{2 \cdot 5} \cdot \frac{5}{\sqrt{10}}$

Step 3.4

Rewrite the expression.

$\frac{- \sqrt{10}}{5} \cdot \frac{5}{\sqrt{10}}$

Step 4

Cancel the common factor of $\sqrt{10}$ .

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Step 4.1

Factor $\sqrt{10}$ out of $- \sqrt{10}$ .

$\frac{\sqrt{10} \cdot - 1}{5} \cdot \frac{5}{\sqrt{10}}$

Step 4.2

Cancel the common factor.

$\frac{\sqrt{10} \cdot - 1}{5} \cdot \frac{5}{\sqrt{10}}$

Step 4.3

Rewrite the expression.

$\frac{- 1}{5} \cdot 5$

Step 5

Cancel the common factor of $5$ .

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Step 5.1

Cancel the common factor.

$\frac{- 1}{5} \cdot 5$

Step 5.2

Rewrite the expression.

$- 1$