Find the Exact Value cos(2*(5pi)/6)

$\cos (2 \cdot \frac{5 π}{6})$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$\cos (2 \cdot \frac{5 π}{2 (3)})$

Cancel the common factor.

$\cos (2 \cdot \frac{5 π}{2 \cdot 3})$

Rewrite the expression.

$\cos (\frac{5 π}{3})$

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

$\cos (\frac{π}{3})$

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

$\frac{1}{2}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$