Find the Exact Value 2cos((5pi)/3)-sin((5pi)/2)

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

Simplify each term.

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

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

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

$2 (\frac{1}{2}) - \sin (\frac{5 π}{2})$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 (\frac{1}{2}) - \sin (\frac{5 π}{2})$

Rewrite the expression.

$1 - \sin (\frac{5 π}{2})$

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

$1 - \sin (\frac{π}{2})$

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

$1 - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$1 - 1$

Subtract $1$ from $1$ .

$0$