Quadrantal Angles

Definition

Quadrantal angles have terminal sides on the coordinate axes.

Why It Matters

These are the “edge cases” of trigonometry. If you forget that tangent is undefined at $\pi/2$ or that cosine is zero at $3\pi/2$, your calculations will crash with division-by-zero errors or return nonsensical values. They are the specific coordinates where the reference triangle collapses, requiring a separate logical branch in your thinking and programming.

Core Concepts

• Examples include $0$, $\pi/2$, $\pi$, $3\pi/2$, and $2\pi$. Some trig functions are undefined there because a denominator is zero.
• How to read: “The zero, pi divided by 2, pi, three pi divided by 2, and two pi.”
  • Meaning: Terminal side lies on an axis—sine or cosine hits 0 or $\pm 1$, making some ratios undefined.
• This concept is part of the chapter-by-chapter synthesis from Trigonometry For Dummies.
• It should be merged with existing math notes if a stronger canonical note already exists.

Connected Concepts

• Trigonometric Functions: Any Angle
• Trigonometric Functions