Final answer:
The exact value of sin(-1320 degrees) is 1.
Therefore, the exact value of sin(-1320 degrees) is 1.
Step-by-step explanation:
To find the exact value of the trig ratio without using a calculator for sin(-1320 degrees), we need to determine the reference angle associated with -1320 degrees and determine the sign of the sin ratio for that angle.
Since -1320 degrees goes beyond a full rotation, we can subtract a multiple of 360 degrees to find its equivalent angle within a full rotation. -1320 degrees = -1320 degrees - (3 * 360 degrees) = -1320 degrees + 1080 degrees = -240 degrees.
Now, we can use the unit circle to find the reference angle of 240 degrees. Since sin is positive in the second quadrant, and the reference angle of 240 degrees is in the second quadrant, the sin ratio is positive.
Therefore, the exact value of sin(-1320 degrees) is 1.