Math
Tangent graphs.
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
Real-world.
- 1 The graph of y = tan(x) repeats every π units along the x-axis
- 2 Vertical asymptotes of y = tan(x) occur at x = π/2 + nπ for any integer n
- 3 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