Trigonometry Examples

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

Step 1

Apply the product rule to $\frac{1}{2}$ .

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

Step 2

One to any power is one.

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

Step 3

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

$\sqrt{1 - \frac{1}{4}}$

Step 4

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

$\sqrt{\frac{4}{4} - \frac{1}{4}}$

Step 5

Combine the numerators over the common denominator.

$\sqrt{\frac{4 - 1}{4}}$

Step 6

Subtract $1$ from $4$ .

$\sqrt{\frac{3}{4}}$

Step 7

Rewrite $\sqrt{\frac{3}{4}}$ as $\frac{\sqrt{3}}{\sqrt{4}}$ .

$\frac{\sqrt{3}}{\sqrt{4}}$

Step 8

Simplify the denominator.

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Step 8.1

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

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

Step 8.2

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

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

Step 9

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.86602540 \dots$