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Common Mistakes

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Frequent Errors

1. Period = 2 pi for tangent instead of pi (3.8.B.1). 2. Asymptotes at k pi instead of pi/2 + k pi (3.8.B.2). 3. tan theta = sin theta (forget cos denominator) (3.8.A.2). 4. Phase shift reported as +c for tan(theta + c) (3.8.C.2). 5. Evaluating tan at pi/2 where cos = 0. 6. Horizontal period formula pi|b| instead of pi/|b| (3.8.C.4). 7. Ignoring reflection when a < 0 or b < 0 (3.8.C.3/C.4). 8. Sketching without vertical asymptotes labeled.

Why These Happen

Students import sine/cosine habits (2 pi period) and miss the cos = 0 restriction unique to tangent.

How to Fix Them

  • Say "tangent period is half of sine's."
  • Mark cos = 0 angles before evaluating.
  • Factor b(theta + c) before reading phase.

Avoidance Scripts

  • "Asymptotes where cos = 0."
  • "Period pi divided by |b|."
  • "Phase -c for (theta + c)."

Quick Self-Check

  • Is my period pi/|b|?
  • Are asymptotes pi/2 + k pi (after phase)?
  • Did I avoid cos = 0 inputs?

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