Trigonometry Examples

$\sqrt{\frac{1 - 2 (\frac{1}{4})}{2}}$

Step 1

Cancel the common factor of $2$ .

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Step 1.1

Factor $2$ out of $- 2$ .

$\sqrt{\frac{1 + 2 (- 1) \frac{1}{4}}{2}}$

Step 1.2

Factor $2$ out of $4$ .

$\sqrt{\frac{1 + 2 \cdot - 1 \frac{1}{2 \cdot 2}}{2}}$

Step 1.3

Cancel the common factor.

$\sqrt{\frac{1 + 2 \cdot - 1 \frac{1}{2 \cdot 2}}{2}}$

Step 1.4

Rewrite the expression.

$\sqrt{\frac{1 - 1 (\frac{1}{2})}{2}}$

Step 2

Simplify the expression.

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Step 2.1

Rewrite $- 1 (\frac{1}{2})$ as $- (\frac{1}{2})$ .

$\sqrt{\frac{1 - (\frac{1}{2})}{2}}$

Step 2.2

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

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

Step 2.3

Combine the numerators over the common denominator.

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

Step 2.4

Subtract $1$ from $2$ .

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

Step 3

Multiply the numerator by the reciprocal of the denominator.

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

Step 4

Multiply $\frac{1}{2} \cdot \frac{1}{2}$ .

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Step 4.1

Multiply $\frac{1}{2}$ by $\frac{1}{2}$ .

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

Step 4.2

Multiply $2$ by $2$ .

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

Step 5

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

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

Step 6

Any root of $1$ is $1$ .

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

Step 7

Simplify the denominator.

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Step 7.1

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

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

Step 7.2

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

$\frac{1}{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$