Trigonometry Examples

$\cos (\frac{π}{6}) \cos (\frac{π}{3}) - \sin (\frac{π}{6}) \sin (\frac{π}{3})$

Step 1

Simplify each term.

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Step 1.1

The exact value of $\cos (\frac{π}{6})$ is $\frac{\sqrt{3}}{2}$ .

$\frac{\sqrt{3}}{2} \cos (\frac{π}{3}) - \sin (\frac{π}{6}) \sin (\frac{π}{3})$

Step 1.2

The exact value of $\cos (\frac{π}{3})$ is $\frac{1}{2}$ .

$\frac{\sqrt{3}}{2} \cdot \frac{1}{2} - \sin (\frac{π}{6}) \sin (\frac{π}{3})$

Step 1.3

Multiply $\frac{\sqrt{3}}{2} \cdot \frac{1}{2}$ .

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Step 1.3.1

Multiply $\frac{\sqrt{3}}{2}$ by $\frac{1}{2}$ .

$\frac{\sqrt{3}}{2 \cdot 2} - \sin (\frac{π}{6}) \sin (\frac{π}{3})$

Step 1.3.2

Multiply $2$ by $2$ .

$\frac{\sqrt{3}}{4} - \sin (\frac{π}{6}) \sin (\frac{π}{3})$

Step 1.4

The exact value of $\sin (\frac{π}{6})$ is $\frac{1}{2}$ .

$\frac{\sqrt{3}}{4} - \frac{1}{2} \sin (\frac{π}{3})$

Step 1.5

The exact value of $\sin (\frac{π}{3})$ is $\frac{\sqrt{3}}{2}$ .

$\frac{\sqrt{3}}{4} - \frac{1}{2} \cdot \frac{\sqrt{3}}{2}$

Step 1.6

Multiply $- \frac{1}{2} \cdot \frac{\sqrt{3}}{2}$ .

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Step 1.6.1

Multiply $\frac{\sqrt{3}}{2}$ by $\frac{1}{2}$ .

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

Step 1.6.2

Multiply $2$ by $2$ .

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

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

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

Step 2.2

Subtract $\sqrt{3}$ from $\sqrt{3}$ .

$\frac{0}{4}$

Step 2.3

Divide $0$ by $4$ .

$0$