Family Overview

In Plain Language

Topic 3.11 covers secant, cosecant, and cotangent—reciprocals of cos, sin, and tan.

• sec: 1/cos; undefined when cos = 0 (3.11.A.1).
• csc: 1/sin; undefined when sin = 0 (3.11.A.2).
• cot: 1/tan; also cos/sin where sin != 0 (3.11.A.4).
• Graphs: sec/csc have asymptotes at cos/sin zeros and range |y| >= 1; cot has asymptotes where sin = 0 and decreases between them (3.11.A.3/A.5).

Why It Matters

Reciprocal trig completes the ratio family and shows up in graph analysis and later identities (3.12).

How Families Can Help

• Ask: "Where does the denominator equal zero?"
• Compare sec/csc graphs to cos/sin—peaks become valleys approach asymptotes.
• Note cot is like tan flipped/reciprocal with different asymptotes.

What Not to Do

• Do not evaluate sec/csc/cot where cos/sin/tan is zero.
• Do not assume sec/csc outputs can be between -1 and 1.
• Do not graph reciprocals without marking asymptotes.