Trigonometry Examples

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

Step 1

Multiply $- (- \frac{1}{2})$ .

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Step 1.1

Multiply $- 1$ by $- 1$ .

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

Step 1.2

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

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

Step 2

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

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Add $2$ and $1$ .

$\sqrt{\frac{\frac{3}{2}}{1 - \frac{1}{2}}}$

Step 5

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

$\sqrt{\frac{\frac{3}{2}}{\frac{2}{2} - \frac{1}{2}}}$

Step 6

Combine the numerators over the common denominator.

$\sqrt{\frac{\frac{3}{2}}{\frac{2 - 1}{2}}}$

Step 7

Subtract $1$ from $2$ .

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

Step 8

Multiply the numerator by the reciprocal of the denominator.

$\sqrt{\frac{3}{2} \cdot 2}$

Step 9

Cancel the common factor of $2$ .

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Step 9.1

Cancel the common factor.

$\sqrt{\frac{3}{2} \cdot 2}$

Step 9.2

Rewrite the expression.

$\sqrt{3}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\sqrt{3}$

Decimal Form:

$1.73205080 \dots$