Final answer:
The value of sin(θ) where θ intersects the unit circle at (12/37, -35/37) is -35/37, since the y-coordinate represents the sine value on the unit circle.
Step-by-step explanation:
To find the value of sin(θ) when the terminal side of an angle θ in standard position intersects the unit circle at the point (12/37, –35/37), we recall that on the unit circle, the y-coordinate of the point gives the value of the sine of the angle. Therefore, the value of sin(θ) is the y-coordinate of the point where the terminal side intersects the unit circle.
In this case, the y-coordinate is -35/37. Hence, sin(θ) = -35/37.
Remember that the range of the sine function is from -1 to 1 and that it represents the ratio of the length of the side opposite to the angle to the hypotenuse in a right-angle triangle. This concept is depicted in trigonometry and unit circle frameworks, as the sine function correlates with the vertical coordinate of a unit circle.