Question

How to find vertical asymptotes of tangent?

Answer 1

To find vertical asymptotes of a tangent function, determine where the tangent function is undefined, which occurs at the solutions of the equation cos(x) = 0. These solutions represent the values of x at which the tangent function has vertical asymptotes.

Step-by-step explanation:

To find vertical asymptotes of a tangent function, we need to determine where the tangent function is undefined. Tangent function is undefined at the values where cosine equals zero. Therefore, the vertical asymptotes of tangent occur at the solutions of the equation cos(x) = 0.

For example, let's find the vertical asymptotes of the tangent function f(x) = tan(x).

1. Solve the equation cos(x) = 0. The solutions to this equation are x = (2n + 1) * (Pi/2), where n is an integer.
2. These solutions represent the values of x at which the tangent function is undefined, leading to vertical asymptotes.

Therefore, the vertical asymptotes of the tangent function are at x = (2n + 1) * (Pi/2), where n is an integer.