Precalculus Examples

$\cos (- 2 π + \frac{π}{6})$

Step 1

To write $- 2 π$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

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

Step 2

Combine fractions.

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Step 2.1

Combine $- 2 π$ and $\frac{6}{6}$ .

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

Step 2.2

Combine the numerators over the common denominator.

$\cos (\frac{- 2 π \cdot 6 + π}{6})$

Step 3

Simplify the numerator.

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Step 3.1

Multiply $6$ by $- 2$ .

$\cos (\frac{- 12 π + π}{6})$

Step 3.2

Add $- 12 π$ and $π$ .

$\cos (\frac{- 11 π}{6})$

Step 4

Move the negative in front of the fraction.

$\cos (- \frac{11 π}{6})$

Step 5

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$\cos (\frac{π}{6})$

Step 6

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

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.86602540 \dots$