Tangent graphs

Math

Definition

The tangent graph plots y = tan(x) and has a distinctive shape with repeating curves separated by vertical asymptotes. Unlike sine and cosine, tangent has a period of π, no amplitude, and vertical asymptotes wherever cosine equals zero.

Examples

  • The graph of y = tan(x) repeats every π units along the x-axis
  • Vertical asymptotes of y = tan(x) occur at x = π/2 + nπ for any integer n
  • A transformed tangent function like y = 2tan(3x) has a period of π/3
Key Fact

Period of y = tan(bx) is π/|b|; vertical asymptotes occur where cos(x) = 0

Related Terms

Graphing trig functions Asymptotes Sine and cosine graphs Amplitude and period

Study This Concept

Practice tangent graphs with free review games in these units:

Trigonometry Unit 4: Graphing Trig Functions