Trigonometry Examples

$- \frac{14 (\sqrt{4})}{\sqrt{11}}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $4$ as $2^{2}$ .

$- \frac{14 \sqrt{2^{2}}}{\sqrt{11}}$

Step 1.2

Pull terms out from under the radical, assuming positive real numbers.

$- \frac{14 \cdot 2}{\sqrt{11}}$

Step 2

Multiply $14$ by $2$ .

$- \frac{28}{\sqrt{11}}$

Step 3

Multiply $\frac{28}{\sqrt{11}}$ by $\frac{\sqrt{11}}{\sqrt{11}}$ .

$- (\frac{28}{\sqrt{11}} \cdot \frac{\sqrt{11}}{\sqrt{11}})$

Step 4

Combine and simplify the denominator.

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Step 4.1

Multiply $\frac{28}{\sqrt{11}}$ by $\frac{\sqrt{11}}{\sqrt{11}}$ .

$- \frac{28 \sqrt{11}}{\sqrt{11} \sqrt{11}}$

Step 4.2

Raise $\sqrt{11}$ to the power of $1$ .

$- \frac{28 \sqrt{11}}{{\sqrt{11}}^{1} \sqrt{11}}$

Step 4.3

Raise $\sqrt{11}$ to the power of $1$ .

$- \frac{28 \sqrt{11}}{{\sqrt{11}}^{1} {\sqrt{11}}^{1}}$

Step 4.4

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

$- \frac{28 \sqrt{11}}{{\sqrt{11}}^{1 + 1}}$

Step 4.5

Add $1$ and $1$ .

$- \frac{28 \sqrt{11}}{{\sqrt{11}}^{2}}$

Step 4.6

Rewrite ${\sqrt{11}}^{2}$ as $11$ .

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Step 4.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{11}$ as $11^{\frac{1}{2}}$ .

$- \frac{28 \sqrt{11}}{{(11^{\frac{1}{2}})}^{2}}$

Step 4.6.2

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

$- \frac{28 \sqrt{11}}{11^{\frac{1}{2} \cdot 2}}$

Step 4.6.3

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

$- \frac{28 \sqrt{11}}{11^{\frac{2}{2}}}$

Step 4.6.4

Cancel the common factor of $2$ .

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Step 4.6.4.1

Cancel the common factor.

$- \frac{28 \sqrt{11}}{11^{\frac{2}{2}}}$

Step 4.6.4.2

Rewrite the expression.

$- \frac{28 \sqrt{11}}{11^{1}}$

Step 4.6.5

Evaluate the exponent.

$- \frac{28 \sqrt{11}}{11}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{28 \sqrt{11}}{11}$

Decimal Form:

$- 8.44231764 \dots$