Final answer:
To find the asymptotes of the tangent (tan) function, identify the values of x for which the tangent function is undefined. These values occur when cos(x) = 0, which happens at x = π/2 + πn, where n is an integer. The correct answer is option D.
Step-by-step explanation:
To find the asymptotes of the tangent (tan) function, you can identify the values of x for which the tangent function is undefined. The tangent function is undefined at values of x where the cosine function is equal to zero. So, the vertical asymptotes of the tangent function occur when cos(x) = 0. This happens when x is equal to π/2 + πn, where n is an integer. To find the asymptotes of the tangent function, you should look for the values of x where the function is undefined.
This happens precisely when the cosine function equals zero because the tangent of an angle is defined as the sine of that angle divided by the cosine of that angle. So, the vertical asymptotes of the tangent function occur at values of x where cos(x) = 0, which happens at odd multiples of π/2, or (2n+1)π/2, where n is an integer. The correct answer to the question is therefore option D: By identifying the values of x for which the tangent function is undefined.