Find the Exact Value cos((3pi)/2)-sin((17pi)/6)

$\cos (\frac{3 π}{2}) - \sin (\frac{17 π}{6})$

Step 1

Simplify each term.

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

$\cos (\frac{π}{2}) - \sin (\frac{17 π}{6})$

The exact value of $\cos (\frac{π}{2})$ is $0$ .

$0 - \sin (\frac{17 π}{6})$

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

$0 - \sin (\frac{5 π}{6})$

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

$0 - \sin (\frac{π}{6})$

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

$0 - \frac{1}{2}$

Step 2

Subtract $\frac{1}{2}$ from $0$ .

$- \frac{1}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{2}$

Decimal Form:

$- 0.5$