Trigonometry Examples

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

Step 1

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

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Simplify the numerator.

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Step 3.1

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

$\sqrt{\frac{4 + 1}{2^{2}}}$

Step 3.2

Add $4$ and $1$ .

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

Step 4

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

$\sqrt{\frac{5}{4}}$

Step 5

Rewrite $\sqrt{\frac{5}{4}}$ as $\frac{\sqrt{5}}{\sqrt{4}}$ .

$\frac{\sqrt{5}}{\sqrt{4}}$

Step 6

Simplify the denominator.

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Step 6.1

Rewrite $4$ as $2^{2}$ .

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

Step 6.2

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

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$1.11803398 \dots$