What is the range of the cosine function?

The cosine function, often denoted as cos(x), oscillates between specific values as its input x varies. The function is defined for all real numbers, meaning that it can take any real number as its input, but the output values it produces are contained within a limited range.

For the cosine function, the maximum value it can reach is 1 and the minimum value it can reach is -1. This means that no matter what angle you use as input, the cosine value will always be within the interval from -1 to 1, inclusive. When visualized on a graph, you would see that the curve of the cosine function never exceeds these bounds, resulting in a range expressed mathematically as [-1, 1].

This characteristic is essential in various fields such as physics and engineering, where understanding the limits of oscillating functions is crucial for calculations and modeling real-world phenomena. So, recognizing that the cosine function effectively maps input angles to outputs strictly within the interval between -1 and 1 confirms that the correct answer articulates this fundamental property of trigonometric functions.