Study Guide
Pre-calculus · AP
AP-aligned materials for 3.6 (Trigonometric and Polar Functions). This topic is assessed on the AP Exam.
What this standard means
- Sinusoidal Function Transformations 1 b 1 2 b The graph of the multiplicative transformation g ( ) = sin(b ) of the sine function f ( ) = sin is a horizontal dilation of the graph of f and differs in period by a factor of . The same transformation of the cosine function yields the same result. 3.6.A.6 The graph of y = f ( ) = asin(b( + c)) + d has an amplitude of a units, a period of units, a midline vertical shift of d units from y = 0, and a phase shift of −c units. The same transformations of the cosine function yield the same results.
- Demonstrate mastery on AP Exam-style questions for this topic.
_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 3.6.
- [ ] 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