Precalculus Examples

$2 \cos (\frac{π}{6}) + \sin (2 \cdot \frac{π}{6})$

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Cancel the common factor.

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

Step 1.2.2

Rewrite the expression.

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

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Factor $2$ out of $6$ .

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

Step 1.3.2

Cancel the common factor.

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

Step 1.3.3

Rewrite the expression.

$\sqrt{3} + \sin (\frac{π}{3})$

Step 1.4

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

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

Step 2

To write $\sqrt{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 3

Combine fractions.

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Step 3.1

Combine $\sqrt{3}$ and $\frac{2}{2}$ .

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

Step 3.2

Combine the numerators over the common denominator.

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

Step 4

Simplify the numerator.

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Step 4.1

Move $2$ to the left of $\sqrt{3}$ .

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

Step 4.2

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

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$2.59807621 \dots$