Trigonometry Examples

$\sin (\frac{π}{4}) \cos (\frac{π}{3}) - \tan (\frac{π}{3})$

Step 1

The exact value of $\sin (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

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

Step 2

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Multiply $2$ by $2$ .

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

Step 4

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

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 1.37849741 \dots$