Trigonometry Examples

$\sqrt{\frac{1 - \frac{3}{5}}{1 + \frac{3}{5}}}$

Step 1

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

$\sqrt{\frac{\frac{5}{5} - \frac{3}{5}}{1 + \frac{3}{5}}}$

Step 2

Combine the numerators over the common denominator.

$\sqrt{\frac{\frac{5 - 3}{5}}{1 + \frac{3}{5}}}$

Step 3

Subtract $3$ from $5$ .

$\sqrt{\frac{\frac{2}{5}}{1 + \frac{3}{5}}}$

Step 4

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

$\sqrt{\frac{\frac{2}{5}}{\frac{5}{5} + \frac{3}{5}}}$

Step 5

Combine the numerators over the common denominator.

$\sqrt{\frac{\frac{2}{5}}{\frac{5 + 3}{5}}}$

Step 6

Add $5$ and $3$ .

$\sqrt{\frac{\frac{2}{5}}{\frac{8}{5}}}$

Step 7

Multiply the numerator by the reciprocal of the denominator.

$\sqrt{\frac{2}{5} \cdot \frac{5}{8}}$

Step 8

Cancel the common factor of $2$ .

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Step 8.1

Factor $2$ out of $8$ .

$\sqrt{\frac{2}{5} \cdot \frac{5}{2 (4)}}$

Step 8.2

Cancel the common factor.

$\sqrt{\frac{2}{5} \cdot \frac{5}{2 \cdot 4}}$

Step 8.3

Rewrite the expression.

$\sqrt{\frac{1}{5} \cdot \frac{5}{4}}$

Step 9

Cancel the common factor of $5$ .

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Step 9.1

Cancel the common factor.

$\sqrt{\frac{1}{5} \cdot \frac{5}{4}}$

Step 9.2

Rewrite the expression.

$\sqrt{\frac{1}{4}}$

Step 10

Rewrite $\sqrt{\frac{1}{4}}$ as $\frac{\sqrt{1}}{\sqrt{4}}$ .

$\frac{\sqrt{1}}{\sqrt{4}}$

Step 11

Any root of $1$ is $1$ .

$\frac{1}{\sqrt{4}}$

Step 12

Simplify the denominator.

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Step 12.1

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

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

Step 12.2

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

$\frac{1}{2}$

Step 13

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$