Final answer:
The correct range of values for the cosine function, considering its minimum value of -1, is -1 < cos < 0. It cannot be less than -1 or greater than 1 as these are its extremal values on the unit circle.
Step-by-step explanation:
The question is asking for the range of values that the cosine function can take. Since the minimum value that the cosine function can reach is -1 and the maximum value is 1, the correct option would be 1) -1 < cos < 0. When the cosine function takes values between -1 and 0, it is negative but greater than its minimum value of -1. On the other hand, it cannot be less than -1, as stated in option 2) cos < -1, because -1 is the minimum value for the cosine function. Similarly, option 3) cos > 1 doesn't hold as 1 is the maximum value of the cosine function and it can never exceed this value. Finally, option 4) 0 < cos < 1 represents the range where the cosine function is positive, but not its entire range.
Additionally, these ranges correspond to different sections of the unit circle where the cosine of an angle is determined by the x-coordinate of the point on the unit circle that intersects with the terminal side of the angle. The cosine of 0° is indeed 1, which aligns with the maximum value.