Trigonometry Examples

$\sqrt{\frac{1 - \frac{24}{25}}{1 + \frac{24}{25}}}$

Step 1

Write $1$ as a fraction with a common denominator.

$\sqrt{\frac{\frac{25}{25} - \frac{24}{25}}{1 + \frac{24}{25}}}$

Step 2

Combine the numerators over the common denominator.

$\sqrt{\frac{\frac{25 - 24}{25}}{1 + \frac{24}{25}}}$

Step 3

Subtract $24$ from $25$ .

$\sqrt{\frac{\frac{1}{25}}{1 + \frac{24}{25}}}$

Step 4

Write $1$ as a fraction with a common denominator.

$\sqrt{\frac{\frac{1}{25}}{\frac{25}{25} + \frac{24}{25}}}$

Step 5

Combine the numerators over the common denominator.

$\sqrt{\frac{\frac{1}{25}}{\frac{25 + 24}{25}}}$

Step 6

Add $25$ and $24$ .

$\sqrt{\frac{\frac{1}{25}}{\frac{49}{25}}}$

Step 7

Multiply the numerator by the reciprocal of the denominator.

$\sqrt{\frac{1}{25} \cdot \frac{25}{49}}$

Step 8

Cancel the common factor of $25$ .

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Step 8.1

Cancel the common factor.

$\sqrt{\frac{1}{25} \cdot \frac{25}{49}}$

Step 8.2

Rewrite the expression.

$\sqrt{\frac{1}{49}}$

Step 9

Rewrite $\sqrt{\frac{1}{49}}$ as $\frac{\sqrt{1}}{\sqrt{49}}$ .

$\frac{\sqrt{1}}{\sqrt{49}}$

Step 10

Any root of $1$ is $1$ .

$\frac{1}{\sqrt{49}}$

Step 11

Simplify the denominator.

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Step 11.1

Rewrite $49$ as $7^{2}$ .

$\frac{1}{\sqrt{7^{2}}}$

Step 11.2

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

$\frac{1}{7}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{7}$

Decimal Form:

$0.\overline{142857}$