Evaluate. Write your answer in simplified, rationalized form. Do not round.sin315°=

The sine of 315 degrees can be found using the unit circle or the sine function's periodic properties.

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

Step 2: Subtract multiples of 360 degrees from 315 degrees until you get an angle that's between 0 and 360 degrees. In this case, 315 degrees is already within this range.

Step 3: Recognize that 315 degrees is 45 degrees away from 360 degrees (or 0 degrees), so sin(315 degrees) = sin(360 degrees - 45 degrees).

Step 4: Use the property that sin(360 degrees - theta) = -sin(theta) to find that sin(315 degrees) = -sin(45 degrees).

Step 5: Recall that sin(45 degrees) = sqrt(2)/2.

Step 6: Substitute sqrt(2)/2 into the equation from step 4 to get sin(315 degrees) = -sqrt(2)/2.

So, sin(315°) = -sqrt(2)/2.