If tan x = 0, which statement about x is true?

If tan x = 0, which statement about x is true?

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

Answer: (A)

tan x equals sin x divided by cos x, so it is zero exactly when the numerator sin x is zero while the denominator cos x is not zero. Sin x is zero at x = nπ for any integer n, and at those angles cos x is not zero, so tan x = 0 there. This means all solutions are x = nπ, which includes x = 0 as the case n = 0, and also π, 2π, -π, etc. The other values don’t work: at x = π/2 the cosine is zero, so tan is undefined; at x = π/4 tan x = 1, not zero. Therefore x = nπ is the correct and complete description of all possible x.

tan x equals sin x divided by cos x, so it is zero exactly when the numerator sin x is zero while the denominator cos x is not zero. Sin x is zero at x = nπ for any integer n, and at those angles cos x is not zero, so tan x = 0 there. This means all solutions are x = nπ, which includes x = 0 as the case n = 0, and also π, 2π, -π, etc. The other values don’t work: at x = π/2 the cosine is zero, so tan is undefined; at x = π/4 tan x = 1, not zero. Therefore x = nπ is the correct and complete description of all possible x.