Find the exact value of sine, 315, degreessin315 ∘ in simplest form with a rational denominator.

The value of sin315° can be found using the unit circle or special triangles.

Step 1: Recognize that 315° is in the fourth quadrant of the unit circle, where sine values are negative.

Step 2: Convert 315° to a reference angle. The reference angle is the acute angle that the terminal side of the given angle makes with the x-axis. For 315°, the reference angle is 360° - 315° = 45°.

Step 3: Find the sine of the reference angle. The sine of 45° is √2/2.

Step 4: Since 315° is in the fourth quadrant where sine is negative, the sine of 315° is -√2/2.

So, sin315° = -√2/2.