Which statement characterizes the tangent function?

Which statement characterizes the tangent function?

• A. It has a period of 180 degrees or π radians and has an asymptote every kπ/2
• B. It has a period of 360 degrees
• C. It is always negative
• D. It has no asymptotes

Answer: (A)

Tangent repeats every 180 degrees and has vertical asymptotes where cosine is zero. Since tan x = sin x / cos x, the period comes from tan(x + π) = tan x, so the period is π radians (180 degrees). The function is undefined at x = π/2 + kπ, which are 90°, 270°, 450°, etc.—points where cosine is zero. Those asymptotes are 180 degrees apart, aligning with the idea of a 180-degree period and regularly spaced vertical asymptotes. This is why the described statement captures the essence of the tangent function. It isn’t correct to say the period is 360 degrees, it isn’t always negative, and there are indeed asymptotes.

Tangent repeats every 180 degrees and has vertical asymptotes where cosine is zero. Since tan x = sin x / cos x, the period comes from tan(x + π) = tan x, so the period is π radians (180 degrees). The function is undefined at x = π/2 + kπ, which are 90°, 270°, 450°, etc.—points where cosine is zero. Those asymptotes are 180 degrees apart, aligning with the idea of a 180-degree period and regularly spaced vertical asymptotes. This is why the described statement captures the essence of the tangent function. It isn’t correct to say the period is 360 degrees, it isn’t always negative, and there are indeed asymptotes.