Study Guide
Learning Objectives
- Define a sinusoidal function (3.5.A.1).
- Relate period and frequency; know parent period $2\pi$ (3.5.A.2).
- Compute amplitude from max/min (3.5.A.3).
- Find the midline as the average of max and min (3.5.A.4).
- Describe concavity oscillation along the wave (3.5.A.5).
- Classify $y=\sin\theta$ as odd and $y=\cos\theta$ as even (3.5.A.6).
Suggested Practice Sequence
1. Label max, min, midline, amplitude on parent graphs. 2. Mark one full period; compute frequency. 3. Compare sine (odd) vs cosine (even) with symmetry tests. 4. Describe where the graph is concave up vs down over a period. 5. Given max/min only, recover midline and amplitude. 6. Preview: transformed waves are still sinusoidal (full details in 3.6).
Classroom / Check-In Moves
- "Max/min $\rightarrow$ midline/amplitude" race.
- Odd/even card sort with sample points.
- Concavity color-coding along one cycle.
Misconception Watch-List
- Amplitude $=$ maximum (fails when midline $\neq 0$).
- Period $=$ distance between consecutive zeros always (not always half-period cues).
- Mixing odd/even.
- Thinking frequency is the same as period.
Vocabulary to Own
- sinusoidal function
- period; frequency
- amplitude; midline
- concave up / concave down
- odd function; even function
- rotational symmetry; reflective symmetry
Materials Map
- Practice: identify characteristics
- Word: wave contexts with max/min
- Mixed / multi-*: link to 3.4 graphs
- Review & practice test: characteristic fluency
- Interactive: period/amplitude/odd-even checks