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Common Mistakes

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Frequent Errors

1. Stopping after one inverse-trig answer (3.10.A.1). 2. Missing symmetric solutions on [0, 2 pi) (3.10.A.2). 3. Listing solutions outside the stated interval. 4. Ignoring contextual domain that limits answers (3.10.A.3). 5. Inequality solution written as single angles instead of intervals. 6. Using wrong period (pi vs 2 pi) when adding k terms. 7. No substitution check after solving. 8. Applying inverse trig without domain validity for sin/cos inputs.

Why These Happen

Periodicity and multiple representations make it easy to lose track of the full solution set or the context window.

How to Fix Them

  • Draw one period and mark all intersection points.
  • Write "principal + symmetry + k*period" workflow explicitly.
  • Substitute each candidate solution.
  • Re-read the context for allowed times/angles.

Avoidance Scripts

  • "Interval first; count solutions on it."
  • "Inverse gives a start, not always the finish."
  • "Context may throw some math answers away."

Quick Self-Check

  • Did I find all solutions on the interval?
  • Did I express inequalities as intervals?
  • Did context eliminate any candidates?

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