Study Guide
Learning Objectives
- Construct analytical and graphical inverse trig representations (3.9.A.1).
- Use arcsin, arccos, arctan notation and know why domains restrict (3.9.A.2).
- State restricted domains for sine, cosine, tangent before inverting (3.9.A.3).
Suggested Practice Sequence
1. Review forward sin/cos/tan values on the unit circle (3.2-3.3). 2. Learn domains and ranges of arcsin, arccos, arctan. 3. Sketch the three inverse graphs on their domains. 4. Evaluate special inverse values; forward-check. 5. Practice compositions and range adjustments.
Classroom / Check-In Moves
- "Domain, range, restriction" three-word check.
- One inverse graph with endpoints labeled.
- Composition exit ticket: sin(arcsin x) vs arcsin(sin x).
Misconception Watch-List
- Using the wrong inverse for a given ratio.
- Forgetting [-1, 1] domain for arcsin/arccos.
- Ignoring arccos range [0, pi].
- Treating inverse output without checking angle mode.
Vocabulary to Own
- arcsin; arccos; arctan; inverse function
- restricted domain; range branch
- composition; angle measure
- sin^-1 x notation (not multiplicative inverse)
Materials Map
- Practice: domains, ranges, graphs, values
- Word: angle-from-ratio contexts
- Mixed / multi-*: link to 3.3, 3.8
- Review & practice test: inverse fluency
- Interactive: domain/range checks