Trigonometry Examples

$\frac{5 \sqrt{26}}{26}$

Step 1

To find the reciprocal, divide $1$ by the number given.

$\frac{1}{\frac{5 \sqrt{26}}{26}}$

Step 2

Simplify.

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Step 2.1

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{26}{5 \sqrt{26}}$

Step 2.2

Multiply $\frac{26}{5 \sqrt{26}}$ by $1$ .

$\frac{26}{5 \sqrt{26}}$

Step 2.3

Multiply $\frac{26}{5 \sqrt{26}}$ by $\frac{\sqrt{26}}{\sqrt{26}}$ .

$\frac{26}{5 \sqrt{26}} \cdot \frac{\sqrt{26}}{\sqrt{26}}$

Step 2.4

Combine and simplify the denominator.

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Step 2.4.1

Multiply $\frac{26}{5 \sqrt{26}}$ by $\frac{\sqrt{26}}{\sqrt{26}}$ .

$\frac{26 \sqrt{26}}{5 \sqrt{26} \sqrt{26}}$

Step 2.4.2

Move $\sqrt{26}$ .

$\frac{26 \sqrt{26}}{5 (\sqrt{26} \sqrt{26})}$

Step 2.4.3

Raise $\sqrt{26}$ to the power of $1$ .

$\frac{26 \sqrt{26}}{5 ({\sqrt{26}}^{1} \sqrt{26})}$

Step 2.4.4

Raise $\sqrt{26}$ to the power of $1$ .

$\frac{26 \sqrt{26}}{5 ({\sqrt{26}}^{1} {\sqrt{26}}^{1})}$

Step 2.4.5

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

$\frac{26 \sqrt{26}}{5 {\sqrt{26}}^{1 + 1}}$

Step 2.4.6

Add $1$ and $1$ .

$\frac{26 \sqrt{26}}{5 {\sqrt{26}}^{2}}$

Step 2.4.7

Rewrite ${\sqrt{26}}^{2}$ as $26$ .

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Step 2.4.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{26}$ as $26^{\frac{1}{2}}$ .

$\frac{26 \sqrt{26}}{5 {(26^{\frac{1}{2}})}^{2}}$

Step 2.4.7.2

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

$\frac{26 \sqrt{26}}{5 \cdot 26^{\frac{1}{2} \cdot 2}}$

Step 2.4.7.3

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

$\frac{26 \sqrt{26}}{5 \cdot 26^{\frac{2}{2}}}$

Step 2.4.7.4

Cancel the common factor of $2$ .

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Step 2.4.7.4.1

Cancel the common factor.

$\frac{26 \sqrt{26}}{5 \cdot 26^{\frac{2}{2}}}$

Step 2.4.7.4.2

Rewrite the expression.

$\frac{26 \sqrt{26}}{5 \cdot 26^{1}}$

Step 2.4.7.5

Evaluate the exponent.

$\frac{26 \sqrt{26}}{5 \cdot 26}$

Step 2.5

Cancel the common factor of $26$ .

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Step 2.5.1

Cancel the common factor.

$\frac{26 \sqrt{26}}{5 \cdot 26}$

Step 2.5.2

Rewrite the expression.

$\frac{\sqrt{26}}{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{26}}{5}$

Decimal Form:

$1.01980390 \dots$