Study Guide — Trigonometric and Polar Functions
Pre-calculus · AP
AP-aligned study guide for Trigonometric and Polar Functions.
What this standard means
- Periodic Phenomena Construct graphs of periodic relationships based on verbal representations.
- Sine, Cosine, and Tangent Determine the sine, cosine, and tangent of an angle using the unit circle.
- Sine and Cosine Function Values Construct representations of the sine and cosine functions using the unit circle.
- Sine and Cosine Function Graphs cos = sin + . 2 2 . Identify key characteristics
- Sinusoidal Functions − 2 The graph of the additive transformation g ( ) = sin + d of the sine function f ( ) = sin is a vertical translation
- Sinusoidal Function Transformations 1 b 1 2 b The graph of the multiplicative transformation g ( ) = sin(b ) of the sine function f ( ) = si
_See printable PDF for diagram._
How to use the 20 practice sets
| Sets | When to use | | --- | --- | | 1–5 | Intro — explore together, short written items | | 6–10 | Core skills — diagrams and written practice | | 11–15 | Mixed review — explain thinking | | 16–20 | Stretch — word problems and mastery tasks |
Pacing: 10–15 minutes per session.
How to practice
1. Label unit circle coordinates for key angles 2. Connect radians and degrees 3. Graph sine and cosine with amplitude and period
_See printable PDF for diagram._
Common mistakes
- Wrong quadrant signs
- Period or amplitude errors in graphs
Review and practice tests
1. Start Review 1/10 when sets 1–3 feel comfortable. 2. Move up one review level with little help. 3. Use Practice Test 4/10–6/10 for mid-standard checks. 4. Practice Test 10/10 is the mastery bar for Trigonometric and Polar Functions.
- [ ] Evaluates trig functions at standard angles
- [ ] Uses unit circle reasoning
- [ ] Graphs basic trig functions with transformations
Materials for this standard
- Practice Problems — 20 printable sets
- Review — 10 difficulty levels
- Practice Test — 10 difficulty levels
- Answer key — for parents and tutors