Study Guide
Learning Objectives
- Place angles in standard position; identify terminal rays and coterminal angles (3.2.A.1).
- Interpret radian measure, especially on the unit circle (3.2.A.2).
- Find $\sin\theta$ and $\cos\theta$ from point $P$ on a circle centered at the origin (3.2.A.3–A.4).
- Find $\tan\theta$ as slope $y/x$ or $\sin/\cos$ when defined (3.2.A.5).
Suggested Practice Sequence
1. Sketch standard position; positive vs negative rotation. 2. Name coterminal angles ($\pm 2\pi$ or $\pm 360^\circ$). 3. Connect radians to arc length on the unit circle. 4. Read $(x,y)$ on the unit circle $\rightarrow$ $(\cos\theta,\sin\theta)$. 5. Compute $\tan\theta=y/x$; note undefined cases. 6. For radius $r\neq 1$, use ratios (displacement over $r$) before specializing to unit circle.
Classroom / Check-In Moves
- Finger trace: "walk the terminal ray; read $x$ and $y$."
- Coterminal bingo ($\theta$ vs $\theta+2\pi$).
- "Is tan defined?" checkpoint on axes.
Misconception Watch-List
- Swapping sine and cosine.
- Thinking radians only exist on the unit circle (ratio idea is general).
- Claiming $\tan$ always exists.
- Treating coterminal angles as "different trig values" (they match for sin/cos/tan).
Vocabulary to Own
- standard position; initial ray; terminal ray
- coterminal angles; revolution
- radian measure; unit circle; arc length
- sine; cosine; tangent; slope of terminal ray
Materials Map
- Practice: definitions and unit-circle reads
- Word: rotation/context stories
- Mixed / multi-*: link to 3.1 period ideas and 3.3 exact values
- Review & practice test: standard position + sin/cos/tan fluency
- Interactive: coordinate and tangent checks