Precalculus Examples

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

Step 1

Simplify each term.

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Step 1.1

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

$2 (\frac{1}{2}) + \cos (\frac{2 π}{6})$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Cancel the common factor.

$2 (\frac{1}{2}) + \cos (\frac{2 π}{6})$

Step 1.2.2

Rewrite the expression.

$1 + \cos (\frac{2 π}{6})$

Step 1.3

Cancel the common factor of $2$ and $6$ .

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Step 1.3.1

Factor $2$ out of $2 π$ .

$1 + \cos (\frac{2 (π)}{6})$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $2$ out of $6$ .

$1 + \cos (\frac{2 π}{2 \cdot 3})$

Step 1.3.2.2

Cancel the common factor.

$1 + \cos (\frac{2 π}{2 \cdot 3})$

Step 1.3.2.3

Rewrite the expression.

$1 + \cos (\frac{π}{3})$

Step 1.4

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

$1 + \frac{1}{2}$

Step 2

Simplify the expression.

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Step 2.1

Write $1$ as a fraction with a common denominator.

$\frac{2}{2} + \frac{1}{2}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{2 + 1}{2}$

Step 2.3

Add $2$ and $1$ .

$\frac{3}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{2}$

Decimal Form:

$1.5$

Mixed Number Form:

$1 \frac{1}{2}$