Trigonometry Examples

$\sqrt{\frac{1 - \frac{- 20}{29}}{1 + \frac{- 20}{29}}}$

Step 1

Move the negative in front of the fraction.

$\sqrt{\frac{1 - - \frac{20}{29}}{1 + \frac{- 20}{29}}}$

Step 2

Multiply $- - \frac{20}{29}$ .

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Step 2.1

Multiply $- 1$ by $- 1$ .

$\sqrt{\frac{1 + 1 (\frac{20}{29})}{1 + \frac{- 20}{29}}}$

Step 2.2

Multiply $\frac{20}{29}$ by $1$ .

$\sqrt{\frac{1 + \frac{20}{29}}{1 + \frac{- 20}{29}}}$

Step 3

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

$\sqrt{\frac{\frac{29}{29} + \frac{20}{29}}{1 + \frac{- 20}{29}}}$

Step 4

Combine the numerators over the common denominator.

$\sqrt{\frac{\frac{29 + 20}{29}}{1 + \frac{- 20}{29}}}$

Step 5

Add $29$ and $20$ .

$\sqrt{\frac{\frac{49}{29}}{1 + \frac{- 20}{29}}}$

Step 6

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

$\sqrt{\frac{\frac{49}{29}}{\frac{29}{29} + \frac{- 20}{29}}}$

Step 7

Combine the numerators over the common denominator.

$\sqrt{\frac{\frac{49}{29}}{\frac{29 - 20}{29}}}$

Step 8

Subtract $20$ from $29$ .

$\sqrt{\frac{\frac{49}{29}}{\frac{9}{29}}}$

Step 9

Multiply the numerator by the reciprocal of the denominator.

$\sqrt{\frac{49}{29} \cdot \frac{29}{9}}$

Step 10

Cancel the common factor of $29$ .

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Step 10.1

Cancel the common factor.

$\sqrt{\frac{49}{29} \cdot \frac{29}{9}}$

Step 10.2

Rewrite the expression.

$\sqrt{49 (\frac{1}{9})}$

Step 11

Combine $49$ and $\frac{1}{9}$ .

$\sqrt{\frac{49}{9}}$

Step 12

Rewrite $\sqrt{\frac{49}{9}}$ as $\frac{\sqrt{49}}{\sqrt{9}}$ .

$\frac{\sqrt{49}}{\sqrt{9}}$

Step 13

Simplify the numerator.

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Step 13.1

Rewrite $49$ as $7^{2}$ .

$\frac{\sqrt{7^{2}}}{\sqrt{9}}$

Step 13.2

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

$\frac{7}{\sqrt{9}}$

Step 14

Simplify the denominator.

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Step 14.1

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

$\frac{7}{\sqrt{3^{2}}}$

Step 14.2

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

$\frac{7}{3}$

Step 15

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{3}$

Decimal Form:

$2.\overline{3}$

Mixed Number Form:

$2 \frac{1}{3}$