Trigonometry Examples

$(\frac{\sqrt{2}}{2}) (\frac{1}{2}) - \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{3}}{2}$

Step 1

Simplify each term.

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Step 1.1

Multiply $(\frac{\sqrt{2}}{2}) (\frac{1}{2})$ .

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Step 1.1.1

Multiply $\frac{\sqrt{2}}{2}$ by $\frac{1}{2}$ .

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

Step 1.1.2

Multiply $2$ by $2$ .

$\frac{\sqrt{2}}{4} - \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{3}}{2}$

Step 1.2

Multiply $- \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{3}}{2}$ .

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Step 1.2.1

Multiply $\frac{\sqrt{3}}{2}$ by $\frac{\sqrt{2}}{2}$ .

$\frac{\sqrt{2}}{4} - \frac{\sqrt{3} \sqrt{2}}{2 \cdot 2}$

Step 1.2.2

Combine using the product rule for radicals.

$\frac{\sqrt{2}}{4} - \frac{\sqrt{3 \cdot 2}}{2 \cdot 2}$

Step 1.2.3

Multiply $3$ by $2$ .

$\frac{\sqrt{2}}{4} - \frac{\sqrt{6}}{2 \cdot 2}$

Step 1.2.4

Multiply $2$ by $2$ .

$\frac{\sqrt{2}}{4} - \frac{\sqrt{6}}{4}$

Step 2

Combine the numerators over the common denominator.

$\frac{\sqrt{2} - \sqrt{6}}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{2} - \sqrt{6}}{4}$

Decimal Form:

$- 0.25881904 \dots$