Precalculus Examples

$4 \tan (\frac{π}{3}) + \cos (\frac{π}{6}) \tan (\frac{π}{6})$

Step 1

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

$4 \sqrt{3} + \cos (\frac{π}{6}) \tan (\frac{π}{6})$

Step 2

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

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Step 2.1

Reorder $\cos (\frac{π}{6})$ and $\tan (\frac{π}{6})$ .

$4 \sqrt{3} + \tan (\frac{π}{6}) \cos (\frac{π}{6})$

Step 2.2

Rewrite $\cos (\frac{π}{6}) \tan (\frac{π}{6})$ in terms of sines and cosines.

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

Step 2.3

Cancel the common factors.

$4 \sqrt{3} + \sin (\frac{π}{6})$

Step 3

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

$4 \sqrt{3} + \frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{3} + \frac{1}{2}$

Decimal Form:

$7.42820323 \dots$