Family Overview

In Plain Language

Topic 3.8 is about the tangent function as slope on the unit circle and as a periodic graph with asymptotes.

• Definition: tan theta is the slope of the terminal ray; also sin theta / cos theta when cos != 0 (3.8.A.1-A.2).
• Key traits: period pi; vertical asymptotes at pi/2 + k pi; increasing on each branch (3.8.B.1-B.3).
• Transforms: vertical/horizontal shifts, dilations, and combined y = a tan(b(theta + c)) + d (3.8.C.1-C.5).

Why It Matters

Tangent completes the core trig trio on the AP exam: students must read asymptotes, period, and transforms—not just sin/cos.

How Families Can Help

• Ask: "What does tan mean as slope on the unit circle?"
• Have them mark where cos = 0 (undefined tan).
• Compare period pi to sin/cos period 2 pi.

What Not to Do

• Do not use period 2 pi for tangent.
• Do not place asymptotes at k pi only (miss pi/2 offset).
• Do not treat tan as sin without dividing by cos.