Trigonometry Examples

$2 \tan (\frac{π}{3}) + \cos (\frac{π}{4}) \tan (\frac{π}{4})$

Step 1

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

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

Step 2

Rewrite in terms of sines and cosines, then cancel the common factors.

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Step 2.1

Reorder $\cos (\frac{π}{4})$ and $\tan (\frac{π}{4})$ .

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

Step 2.2

Rewrite $\cos (\frac{π}{4}) \tan (\frac{π}{4})$ in terms of sines and cosines.

$2 \sqrt{3} + \frac{\sin (\frac{π}{4})}{\cos (\frac{π}{4})} \cos (\frac{π}{4})$

Step 2.3

Cancel the common factors.

$2 \sqrt{3} + \sin (\frac{π}{4})$

Step 3

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

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$4.17120839 \dots$