HUNTERTUTORING
← AP
Get startedBook tutoring

Study Guide

Open PDF

Pre-calculus · AP

AP-aligned materials for 3.13 (Trigonometric and Polar Functions). This topic is assessed on the AP Exam.

What this standard means

  • Trigonometry and Polar Coordinates Construct graphs of polar functions. The graph of the function r = f ( ) in polar coordinates consists of input-output pairs of values where the input values are angle measures and the output values are radii. 3.14.A.2 The domain of the polar function r = f ( ), given graphically, can be restricted to a desired portion of the function by selecting endpoints corresponding to the desired angle and radius. 3.14.A.3 When graphing polar functions in the form of r = f ( ), changes in input values correspond to changes in angle measure from the positive x-axis, and changes in output values correspond to changes in distance from the origin.
  • 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 3.13.

  • [ ] 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.

Back to 3.13