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Common Mistakes

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Frequent Errors

1. Evaluating sec where cos = 0 or csc where sin = 0 (3.11.A.1/A.2). 2. Claiming sec or csc can equal 0.5 (3.11.A.3). 3. Asymptotes for sec/csc at wrong angles (not cos/sin zeros). 4. Graphing sec/csc without gaps at asymptotes. 5. Cot asymptotes at cos = 0 instead of sin = 0 (3.11.A.5). 6. Forgetting cot decreases between asymptotes (3.11.A.5). 7. Confusing cot with tan graph shape. 8. Missing that cot = cos/sin, not sin/cos (3.11.A.4).

Why These Happen

Students focus on forward trig graphs and treat reciprocals as "the same but bigger."

How to Fix Them

  • Always list denominator zeros first.
  • Compare |sec| and |cos| at the same angle.
  • Sketch asymptotes before curves.

Avoidance Scripts

  • "Denominator zero means undefined."
  • "sec/csc live outside (-1, 1)."
  • "cot breaks where sin = 0."

Quick Self-Check

  • Did I check cos != 0 for sec and sin != 0 for csc/cot?
  • Are asymptotes at the right zeros?
  • Is |output| >= 1 for sec/csc when defined?

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