Study Guide
Learning Objectives
- Construct $y=\sin\theta$ from unit-circle $y$-coordinates (3.4.A.1–A.2).
- Construct $y=\cos\theta$ from unit-circle $x$-coordinates (3.4.A.3–A.4).
- State domains (all reals) and oscillation between $-1$ and $1$.
- Match key angles to graph landmarks (intercepts, max, min).
Suggested Practice Sequence
1. Table of exact values from 3.3 for $0$ to $2\pi$. 2. Plot $y=\sin\theta$ from the table; connect smoothly. 3. Plot $y=\cos\theta$ from the same angles. 4. Extend beyond $[0,2\pi]$ using repetition from the circle. 5. Compare: cosine is a horizontal shift of sine (preview, not full 3.6). 6. Given a graph point, find the matching unit-circle point $P$.
Classroom / Check-In Moves
- "Walk the circle, drop the height" (sine) / "drop the width" (cosine).
- Landmark matching cards: $\pi/2$ on circle vs on graph.
- Domain challenge: name an angle outside $[0,2\pi]$ and its sine.
Misconception Watch-List
- Thinking the graph only exists for one revolution.
- Plotting degrees on an axis meant for radians without labeling.
- Mixing $x$- and $y$-coordinates when building the waves.
- Expecting amplitude changes before transformations (those are later topics).
Vocabulary to Own
- sine function; cosine function
- unit circle representation
- oscillate; range $[-1,1]$
- domain of all real numbers
- vertical / horizontal displacement of $P$
Materials Map
- Practice: build and read graphs from the circle
- Word: motion/height stories tied to unwrapping
- Mixed / multi-*: link to 3.2–3.3 values
- Review & practice test: graph construction fluency
- Interactive: landmark and domain checks