Tangent Graph

Definition

The visual representation of the tangent function, which contains discontinuities (vertical asymptotes) where the cosine function equals zero.

Why It Matters

The graph represents the ‘forbidden zones’ of circular motion where values explode toward infinity, essential for managing extreme stress points.

Core Concepts

• Tangent ($y = \tan x$): Period is $\pi$. Vertical asymptotes at odd multiples of $\pi/2$. Range is $(-\infty, \infty)$.
  • How to read: “The value y is equal to the tangent of x.”
  • Meaning: $\tan x = \sin x / \cos x$ — blows up where $\cos x = 0$; period $\pi$; vertical asymptotes at odd multiples of $\pi/2$.

Connected Concepts

• Trigonometric Functions on the Unit Circle
• Vertical Asymptotes