Trigonometry Examples

$\sqrt{{(\frac{13}{12})}^{2} - 1}$

Step 1

Apply the product rule to $\frac{13}{12}$ .

$\sqrt{\frac{13^{2}}{12^{2}} - 1}$

Step 2

Raise $13$ to the power of $2$ .

$\sqrt{\frac{169}{12^{2}} - 1}$

Step 3

Raise $12$ to the power of $2$ .

$\sqrt{\frac{169}{144} - 1}$

Step 4

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{144}{144}$ .

$\sqrt{\frac{169}{144} - 1 \cdot \frac{144}{144}}$

Step 5

Combine $- 1$ and $\frac{144}{144}$ .

$\sqrt{\frac{169}{144} + \frac{- 1 \cdot 144}{144}}$

Step 6

Combine the numerators over the common denominator.

$\sqrt{\frac{169 - 1 \cdot 144}{144}}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $- 1$ by $144$ .

$\sqrt{\frac{169 - 144}{144}}$

Step 7.2

Subtract $144$ from $169$ .

$\sqrt{\frac{25}{144}}$

Step 8

Rewrite $\sqrt{\frac{25}{144}}$ as $\frac{\sqrt{25}}{\sqrt{144}}$ .

$\frac{\sqrt{25}}{\sqrt{144}}$

Step 9

Simplify the numerator.

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Step 9.1

Rewrite $25$ as $5^{2}$ .

$\frac{\sqrt{5^{2}}}{\sqrt{144}}$

Step 9.2

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

$\frac{5}{\sqrt{144}}$

Step 10

Simplify the denominator.

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Step 10.1

Rewrite $144$ as $12^{2}$ .

$\frac{5}{\sqrt{12^{2}}}$

Step 10.2

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

$\frac{5}{12}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{12}$

Decimal Form:

$0.41\overline{6}$