Final answer:
The maximum value of y = sin (0) for angles between -720° and 720° is 1. The sine function's range is from -1 to 1, and it reaches its peak at 90° increments within the given range.
Step-by-step explanation:
The maximum value of y = sin (0) for any angle (denoted as 0 in the question, which seems to be a typo for θ, the Greek letter theta used to represent angles) is 1. This is because the sine function, which represents the ratio of the length of the side opposite the angle to the hypotenuse in a right-angled triangle, has a range between -1 and 1. No matter what the angle is, the sine of the angle will never exceed these bounds.
The question asks for the maximum value of y = sin (0) for angles between –720° and 720°, which spans multiple full rotations on the unit circle. Despite these rotations, the maximum value does not change because the sine function is periodic with a period of 360° (2π radians). Therefore, the maximum value of y is still 1, as it is at 90°, 450°, -270°, etc., which are all angles where the sine function peaks during its cycle.