Trigonometry Examples

$\sqrt{\frac{1 - \frac{7}{25}}{1 + \frac{7}{25}}}$

Step 1

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

$\sqrt{\frac{\frac{25}{25} - \frac{7}{25}}{1 + \frac{7}{25}}}$

Step 2

Combine the numerators over the common denominator.

$\sqrt{\frac{\frac{25 - 7}{25}}{1 + \frac{7}{25}}}$

Step 3

Subtract $7$ from $25$ .

$\sqrt{\frac{\frac{18}{25}}{1 + \frac{7}{25}}}$

Step 4

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

$\sqrt{\frac{\frac{18}{25}}{\frac{25}{25} + \frac{7}{25}}}$

Step 5

Combine the numerators over the common denominator.

$\sqrt{\frac{\frac{18}{25}}{\frac{25 + 7}{25}}}$

Step 6

Add $25$ and $7$ .

$\sqrt{\frac{\frac{18}{25}}{\frac{32}{25}}}$

Step 7

Multiply the numerator by the reciprocal of the denominator.

$\sqrt{\frac{18}{25} \cdot \frac{25}{32}}$

Step 8

Cancel the common factor of $2$ .

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Step 8.1

Factor $2$ out of $18$ .

$\sqrt{\frac{2 (9)}{25} \cdot \frac{25}{32}}$

Step 8.2

Factor $2$ out of $32$ .

$\sqrt{\frac{2 \cdot 9}{25} \cdot \frac{25}{2 \cdot 16}}$

Step 8.3

Cancel the common factor.

$\sqrt{\frac{2 \cdot 9}{25} \cdot \frac{25}{2 \cdot 16}}$

Step 8.4

Rewrite the expression.

$\sqrt{\frac{9}{25} \cdot \frac{25}{16}}$

Step 9

Cancel the common factor of $25$ .

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Step 9.1

Cancel the common factor.

$\sqrt{\frac{9}{25} \cdot \frac{25}{16}}$

Step 9.2

Rewrite the expression.

$\sqrt{9 (\frac{1}{16})}$

Step 10

Combine $9$ and $\frac{1}{16}$ .

$\sqrt{\frac{9}{16}}$

Step 11

Rewrite $\sqrt{\frac{9}{16}}$ as $\frac{\sqrt{9}}{\sqrt{16}}$ .

$\frac{\sqrt{9}}{\sqrt{16}}$

Step 12

Simplify the numerator.

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Step 12.1

Rewrite $9$ as $3^{2}$ .

$\frac{\sqrt{3^{2}}}{\sqrt{16}}$

Step 12.2

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

$\frac{3}{\sqrt{16}}$

Step 13

Simplify the denominator.

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Step 13.1

Rewrite $16$ as $4^{2}$ .

$\frac{3}{\sqrt{4^{2}}}$

Step 13.2

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

$\frac{3}{4}$

Step 14

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{4}$

Decimal Form:

$0.75$