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Common Mistakes

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Frequent Errors

1. Using arcsin when arccos (or arctan) matches the given ratio. 2. Evaluating arcsin/arccos for |x| > 1 (3.9.A.2). 3. Reporting arccos output outside [0, pi] (3.9.A.3). 4. Treating sin^-1 x as 1/sin x (notation trap) (3.9.A.2). 5. Ignoring range when simplifying arcsin(sin x) (3.9.A.3). 6. Forgetting tangent must be restricted to (-pi/2, pi/2) before inverting (3.9.A.3). 7. Calculator in wrong angle mode (degrees vs radians). 8. Skipping domain justification on FRQ items (3.9.A.1).

Why These Happen

Students meet inverse notation late and mix it with reciprocal trig or unrestricted periodic graphs.

How to Fix Them

  • Write domain/range before evaluating.
  • Draw the restricted branch and its inverse together.
  • Forward-check with sin/cos/tan after finding an angle.

Avoidance Scripts

  • "Input in [-1, 1] for arcsin/arccos."
  • "arccos lives on [0, pi]."
  • "sin^-1 means inverse function, not reciprocal."

Quick Self-Check

  • Is my input in the inverse domain?
  • Is my angle in the correct range branch?
  • Did I use the inverse that matches the ratio given?

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