tan x is undefined at which of the following x-values?

tan x is undefined at which of the following x-values?

• A. x = kπ
• B. x = 0
• C. x = π/2 + kπ
• D. x = π/4

Answer: (C)

tan x is sin x divided by cos x, so it’s undefined whenever cos x equals zero. Cosine is zero at x = π/2 + kπ for any integer k, meaning those are the x-values where tan x cannot be defined due to division by zero. That perfectly matches the given option x = π/2 + kπ. Other listed values don’t cause cos x to be zero (for example, at multiples of π, tan x is 0 because sin x is 0; at π/4, tan x is 1).

tan x is sin x divided by cos x, so it’s undefined whenever cos x equals zero. Cosine is zero at x = π/2 + kπ for any integer k, meaning those are the x-values where tan x cannot be defined due to division by zero. That perfectly matches the given option x = π/2 + kπ. Other listed values don’t cause cos x to be zero (for example, at multiples of π, tan x is 0 because sin x is 0; at π/4, tan x is 1).