Trigonometry Examples

$2 (- \frac{6}{\sqrt{61}}) (- \frac{5}{\sqrt{61}})$

Step 1

Multiply $\frac{6}{\sqrt{61}}$ by $\frac{\sqrt{61}}{\sqrt{61}}$ .

$2 (- (\frac{6}{\sqrt{61}} \cdot \frac{\sqrt{61}}{\sqrt{61}})) \cdot (- \frac{5}{\sqrt{61}})$

Step 2

Combine and simplify the denominator.

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Step 2.1

Multiply $\frac{6}{\sqrt{61}}$ by $\frac{\sqrt{61}}{\sqrt{61}}$ .

$2 (- \frac{6 \sqrt{61}}{\sqrt{61} \sqrt{61}}) \cdot (- \frac{5}{\sqrt{61}})$

Step 2.2

Raise $\sqrt{61}$ to the power of $1$ .

$2 (- \frac{6 \sqrt{61}}{{\sqrt{61}}^{1} \sqrt{61}}) \cdot (- \frac{5}{\sqrt{61}})$

Step 2.3

Raise $\sqrt{61}$ to the power of $1$ .

$2 (- \frac{6 \sqrt{61}}{{\sqrt{61}}^{1} {\sqrt{61}}^{1}}) \cdot (- \frac{5}{\sqrt{61}})$

Step 2.4

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

$2 (- \frac{6 \sqrt{61}}{{\sqrt{61}}^{1 + 1}}) \cdot (- \frac{5}{\sqrt{61}})$

Step 2.5

Add $1$ and $1$ .

$2 (- \frac{6 \sqrt{61}}{{\sqrt{61}}^{2}}) \cdot (- \frac{5}{\sqrt{61}})$

Step 2.6

Rewrite ${\sqrt{61}}^{2}$ as $61$ .

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Step 2.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{61}$ as $61^{\frac{1}{2}}$ .

$2 (- \frac{6 \sqrt{61}}{{(61^{\frac{1}{2}})}^{2}}) \cdot (- \frac{5}{\sqrt{61}})$

Step 2.6.2

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

$2 (- \frac{6 \sqrt{61}}{61^{\frac{1}{2} \cdot 2}}) \cdot (- \frac{5}{\sqrt{61}})$

Step 2.6.3

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

$2 (- \frac{6 \sqrt{61}}{61^{\frac{2}{2}}}) \cdot (- \frac{5}{\sqrt{61}})$

Step 2.6.4

Cancel the common factor of $2$ .

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Step 2.6.4.1

Cancel the common factor.

$2 (- \frac{6 \sqrt{61}}{61^{\frac{2}{2}}}) \cdot (- \frac{5}{\sqrt{61}})$

Step 2.6.4.2

Rewrite the expression.

$2 (- \frac{6 \sqrt{61}}{61^{1}}) \cdot (- \frac{5}{\sqrt{61}})$

Step 2.6.5

Evaluate the exponent.

$2 (- \frac{6 \sqrt{61}}{61}) \cdot (- \frac{5}{\sqrt{61}})$

Step 3

Multiply $2 (- \frac{6 \sqrt{61}}{61})$ .

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Step 3.1

Multiply $- 1$ by $2$ .

$- 2 \frac{6 \sqrt{61}}{61} \cdot (- \frac{5}{\sqrt{61}})$

Step 3.2

Combine $- 2$ and $\frac{6 \sqrt{61}}{61}$ .

$\frac{- 2 (6 \sqrt{61})}{61} \cdot (- \frac{5}{\sqrt{61}})$

Step 3.3

Multiply $6$ by $- 2$ .

$\frac{- 12 \sqrt{61}}{61} \cdot (- \frac{5}{\sqrt{61}})$

Step 4

Cancel the common factor of $\sqrt{61}$ .

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Step 4.1

Move the leading negative in $- \frac{5}{\sqrt{61}}$ into the numerator.

$\frac{- 12 \sqrt{61}}{61} \cdot \frac{- 5}{\sqrt{61}}$

Step 4.2

Factor $\sqrt{61}$ out of $- 12 \sqrt{61}$ .

$\frac{\sqrt{61} \cdot - 12}{61} \cdot \frac{- 5}{\sqrt{61}}$

Step 4.3

Cancel the common factor.

$\frac{\sqrt{61} \cdot - 12}{61} \cdot \frac{- 5}{\sqrt{61}}$

Step 4.4

Rewrite the expression.

$\frac{- 12}{61} \cdot - 5$

Step 5

Combine $\frac{- 12}{61}$ and $- 5$ .

$\frac{- 12 \cdot - 5}{61}$

Step 6

Multiply $- 12$ by $- 5$ .

$\frac{60}{61}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{60}{61}$

Decimal Form:

$0.98360655 \dots$