Answer:
Explanation:
The trigonometric function that does not have a period of 2π is the tangent function, denoted by tan(x).
The period of a trigonometric function is the length of one complete cycle of the function. For the sine and cosine functions, the period is always 2π, which means that the function repeats itself every 2π units.
However, the tangent function has a period of π, which means that it repeats itself every π units. This is because the tangent function has vertical asymptotes at x = (n + 1/2)π, where n is an integer, and the function changes sign between these asymptotes. Therefore, the tangent function does not have a period of 2π.