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Pre-calculus · AP

AP-aligned materials for 3.14 (Trigonometric and Polar Functions). This topic is assessed on the AP Exam.

What this standard means

  • Polar Function Graphs Describe characteristics of the graph of a polar function. If a polar function, r = f ( ), is positive and increasing or negative and decreasing, then the distance between f ( ) and the origin is increasing. 3.15.A.2 If a polar function, r = f ( ), is positive and decreasing or negative and increasing, then the distance between f ( ) and the origin is decreasing. 3.15.A.3 For a polar function, r = f ( ), if the function changes from increasing to decreasing or decreasing to increasing on an interval, then the function has a relative extremum on the interval corresponding to a point relatively closest to or farthest from the origin. 3.15.A.4 The average rate of change of r with respect to over an interval of is the ratio of the change in the radius values to the change in over an interval of . Graphically, the average rate of change indicates the rate at which the radius is changing per radian. 3.15.A.5 The average rate of change of r with respect to over an interval of can be used to estimate values of the function within the interval.
  • 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 3.14.

  • [ ] 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

For your personal study only. Copying, printing, screenshotting, or sharing this material is not permitted and may result in loss of access.

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