Algebra Examples

$\tan (\frac{2 π}{3}) + 4 \cos (\frac{11 π}{6})$

Step 1

Simplify each term.

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Step 1.1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because tangent is negative in the second quadrant.

$- \tan (\frac{π}{3}) + 4 \cos (\frac{11 π}{6})$

Step 1.2

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

$- \sqrt{3} + 4 \cos (\frac{11 π}{6})$

Step 1.3

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$- \sqrt{3} + 4 \cos (\frac{π}{6})$

Step 1.4

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

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

Step 1.5

Cancel the common factor of $2$ .

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Step 1.5.1

Factor $2$ out of $4$ .

$- \sqrt{3} + 2 (2) \frac{\sqrt{3}}{2}$

Step 1.5.2

Cancel the common factor.

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

Step 1.5.3

Rewrite the expression.

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

Step 2

Add $- \sqrt{3}$ and $2 \sqrt{3}$ .

$\sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{3}$

Decimal Form:

$1.73205080 \dots$