Trigonometry Examples

$\sqrt{\frac{1 - (\frac{- 5}{6})}{1 + \frac{- 5}{6}}}$

Step 1

Move the negative in front of the fraction.

$\sqrt{\frac{1 - - \frac{5}{6}}{1 + \frac{- 5}{6}}}$

Step 2

Multiply $- - \frac{5}{6}$ .

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Step 2.1

Multiply $- 1$ by $- 1$ .

$\sqrt{\frac{1 + 1 (\frac{5}{6})}{1 + \frac{- 5}{6}}}$

Step 2.2

Multiply $\frac{5}{6}$ by $1$ .

$\sqrt{\frac{1 + \frac{5}{6}}{1 + \frac{- 5}{6}}}$

Step 3

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

$\sqrt{\frac{\frac{6}{6} + \frac{5}{6}}{1 + \frac{- 5}{6}}}$

Step 4

Combine the numerators over the common denominator.

$\sqrt{\frac{\frac{6 + 5}{6}}{1 + \frac{- 5}{6}}}$

Step 5

Add $6$ and $5$ .

$\sqrt{\frac{\frac{11}{6}}{1 + \frac{- 5}{6}}}$

Step 6

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

$\sqrt{\frac{\frac{11}{6}}{\frac{6}{6} + \frac{- 5}{6}}}$

Step 7

Combine the numerators over the common denominator.

$\sqrt{\frac{\frac{11}{6}}{\frac{6 - 5}{6}}}$

Step 8

Subtract $5$ from $6$ .

$\sqrt{\frac{\frac{11}{6}}{\frac{1}{6}}}$

Step 9

Multiply the numerator by the reciprocal of the denominator.

$\sqrt{\frac{11}{6} \cdot 6}$

Step 10

Cancel the common factor of $6$ .

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Step 10.1

Cancel the common factor.

$\sqrt{\frac{11}{6} \cdot 6}$

Step 10.2

Rewrite the expression.

$\sqrt{11}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\sqrt{11}$

Decimal Form:

$3.31662479 \dots$