Final answer:
To find the vertical asymptotes of the tangent function, we need to determine the values of x at which the tangent function is undefined. These vertical asymptotes occur when cosine x = 0.
Step-by-step explanation:
In order to find the vertical asymptotes of the tangent function, we need to determine the values of x at which the tangent function is undefined. The tangent function is undefined at values where the cosine function, which is in the denominator of the tangent function, equals zero. In other words, the vertical asymptotes occur when cosine x = 0. The solutions to this equation are x = (2n + 1)(π/2), where n is an integer.
For example, if we consider the tangent function y = tan(x), the vertical asymptotes occur at x = (2n + 1)(π/2), where n is any integer. The graph of the tangent function approaches these vertical asymptotes but never crosses them.
For instance, the vertical asymptotes of the tangent function can be found at x = π/2, x = 3π/2, x = 5π/2, and so on. These are vertical lines that the graph of the tangent function approaches but does not intersect.