Trigonometry Examples

$\sqrt{1 - {(\frac{5}{6})}^{2}}$

Step 1

Apply the product rule to $\frac{5}{6}$ .

$\sqrt{1 - \frac{5^{2}}{6^{2}}}$

Step 2

Raise $5$ to the power of $2$ .

$\sqrt{1 - \frac{25}{6^{2}}}$

Step 3

Raise $6$ to the power of $2$ .

$\sqrt{1 - \frac{25}{36}}$

Step 4

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

$\sqrt{\frac{36}{36} - \frac{25}{36}}$

Step 5

Combine the numerators over the common denominator.

$\sqrt{\frac{36 - 25}{36}}$

Step 6

Subtract $25$ from $36$ .

$\sqrt{\frac{11}{36}}$

Step 7

Rewrite $\sqrt{\frac{11}{36}}$ as $\frac{\sqrt{11}}{\sqrt{36}}$ .

$\frac{\sqrt{11}}{\sqrt{36}}$

Step 8

Simplify the denominator.

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Step 8.1

Rewrite $36$ as $6^{2}$ .

$\frac{\sqrt{11}}{\sqrt{6^{2}}}$

Step 8.2

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

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

Step 9

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.55277079 \dots$