Final answer:
The exact value of sin(12/7π) cannot be determined from the provided options, as this is not a standard angle with a well-known sine value. A calculator would be needed for an accurate value. The correct option is A.
Step-by-step explanation:
The exact value of sin(12/7π) is not one of the options provided (A) √2-1/2, B) √3/2, C) 1/√2, D) 1/2), since 12/7π is not a standard angle for which the sine value is commonly known or derived from unit circle values. To evaluate the sine of a non-standard angle like sin(12/7π), you would typically need to use a calculator or numerical methods, as the sine function does not result in simple rational or irrational roots like the given options for such angles.
The exact value of sin(12/7π) is -√2-1/2.
To find this value, we can use the unit circle and the fact that sin is periodic with a period of 2π. So, sin(12/7π) is equivalent to sin(2π + 5/7π).
Since the sine function repeats itself every 2π, we can conclude that sin(2π + 5/7π) = sin(5/7π).
On the unit circle, sin(5/7π) corresponds to the y-coordinate of the point that is 5/7 of the way around the unit circle. This point lies in the third quadrant and has a y-coordinate of -√2/2. Therefore, sin(12/7π) = -√2/2 = -√2-1/2.