Trigonometry Examples

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

Step 1

Move the negative in front of the fraction.

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

Step 2

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

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Step 2.1

Multiply $- 1$ by $2$ .

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

Step 2.2

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

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

Step 2.3

Multiply $6$ by $- 2$ .

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

Step 3

Move the negative in front of the fraction.

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

Step 4

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

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Step 4.1

Multiply $- 1$ by $- 1$ .

$1 \frac{12 \sqrt{61}}{61} \frac{5 \sqrt{61}}{61}$

Step 4.2

Multiply $\frac{12 \sqrt{61}}{61}$ by $1$ .

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

Step 4.3

Multiply $\frac{12 \sqrt{61}}{61}$ by $\frac{5 \sqrt{61}}{61}$ .

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

Step 4.4

Multiply $5$ by $12$ .

$\frac{60 \sqrt{61} \sqrt{61}}{61 \cdot 61}$

Step 4.5

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

$\frac{60 ({\sqrt{61}}^{1} \sqrt{61})}{61 \cdot 61}$

Step 4.6

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

$\frac{60 ({\sqrt{61}}^{1} {\sqrt{61}}^{1})}{61 \cdot 61}$

Step 4.7

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

$\frac{60 {\sqrt{61}}^{1 + 1}}{61 \cdot 61}$

Step 4.8

Add $1$ and $1$ .

$\frac{60 {\sqrt{61}}^{2}}{61 \cdot 61}$

Step 4.9

Multiply $61$ by $61$ .

$\frac{60 {\sqrt{61}}^{2}}{3721}$

Step 5

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

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Step 5.1

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

$\frac{60 {(61^{\frac{1}{2}})}^{2}}{3721}$

Step 5.2

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

$\frac{60 \cdot 61^{\frac{1}{2} \cdot 2}}{3721}$

Step 5.3

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

$\frac{60 \cdot 61^{\frac{2}{2}}}{3721}$

Step 5.4

Cancel the common factor of $2$ .

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Step 5.4.1

Cancel the common factor.

$\frac{60 \cdot 61^{\frac{2}{2}}}{3721}$

Step 5.4.2

Rewrite the expression.

$\frac{60 \cdot 61^{1}}{3721}$

Step 5.5

Evaluate the exponent.

$\frac{60 \cdot 61}{3721}$

Step 6

Multiply $60$ by $61$ .

$\frac{3660}{3721}$

Step 7

Cancel the common factor of $3660$ and $3721$ .

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Step 7.1

Factor $61$ out of $3660$ .

$\frac{61 (60)}{3721}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $61$ out of $3721$ .

$\frac{61 \cdot 60}{61 \cdot 61}$

Step 7.2.2

Cancel the common factor.

$\frac{61 \cdot 60}{61 \cdot 61}$

Step 7.2.3

Rewrite the expression.

$\frac{60}{61}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{60}{61}$

Decimal Form:

$0.98360655 \dots$