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Study Guide

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Learning Objectives

  • Define sec, csc, cot as reciprocals (3.11.A.1, A.2, A.4).
  • Identify asymptotes and range for sec/csc (3.11.A.3).
  • Describe cotangent graph behavior (3.11.A.5).

Suggested Practice Sequence

1. Write definitions with domain restrictions. 2. Mark sin/cos zeros --> asymptotes for sec/csc/cot. 3. Sketch sec, csc, cot on one period each. 4. Evaluate specials when defined; practice undefined checks. 5. Compare graphs to sin/cos/tan (2.B).

Classroom / Check-In Moves

  • "Denominator zero?" before every evaluation.
  • Asymptote drill from unit circle.
  • Range check: can this reciprocal equal 0.5?

Misconception Watch-List

  • Graphing sec like cos (missing U-shapes and gaps).
  • Forgetting |sec|, |csc| >= 1.
  • Cot asymptotes at wrong angles (need sin = 0).
  • Missing that cot decreases on branches.

Vocabulary to Own

  • secant; cosecant; cotangent; reciprocal
  • vertical asymptote; undefined
  • range (-inf, -1] union [1, inf)
  • decreasing branch (cot)

Materials Map

  • Practice: definitions, asymptotes, graphs
  • Word: graph/interpretation contexts
  • Mixed / multi-*: link to 3.3-3.8
  • Review & practice test: trait fluency
  • Interactive: definition/asymptote checks

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