Find the Exact Value sin(-5/4pi)

$\sin (- \frac{5}{4} π)$

Step 1

Combine $π$ and $\frac{5}{4}$ .

$\sin (- \frac{π \cdot 5}{4})$

Step 2

Move $5$ to the left of $π$ .

$\sin (- \frac{5 \cdot π}{4})$

Step 3

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

$\sin (\frac{3 π}{4})$

Step 4

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

$\sin (\frac{π}{4})$

Step 5

The exact value of $\sin (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.70710678 \dots$