---
title: "PC.FGR.3: Trigonometric Modeling Overview (Georgia Mathematics standard)"
code: PC.FGR.3
cite_as: Georgia Standards of Excellence, Mathematics, PC.FGR.3
subject: math
grades:
  - high-school
language: en
canonical_url: https://georgiahomeroom.org/standards/code/PC.FGR.3
md_url: https://georgiahomeroom.org/standards/code/PC.FGR.3.md
alternate_language_url: https://georgiahomeroom.org/es/standards/code/PC.FGR.3.md
source_url: https://case.georgiastandards.org/ims/case/v1p1/CFDocuments/e9dd7229-3558-4df2-85c6-57b8938f6180
source_last_changed: 2024-10-09
data_built: 2026-09-18
publisher: Georgia Homeroom, a free public-interest project of Georgia Civic Data. Not affiliated with or endorsed by the Georgia Department of Education or any school district.
up: https://georgiahomeroom.org/standards/math/high-school.md
index: https://georgiahomeroom.org/standards/index.md
---

# PC.FGR.3: Trigonometric Modeling Overview

Utilize trigonometric expressions to solve problems and model periodic phenomena with trigonometric functions.

- Subject: Mathematics
- Appears in: High School, https://georgiahomeroom.org/standards/math/high-school.md

## Expectations

- Define and analyze trigonometric relationships.
  - **PC.FGR.3.1**: Use the concept of a radian as the ratio of the arc length to the radius of a circle to establish the existence of 2π radians in one revolution.
  - **PC.FGR.3.2**: Utilize right triangles on the unit circle to determine the values of the six trigonometric ratios for $\frac{\pi}{6}$, $\frac{\pi}{4}$, and $\frac{\pi}{3}$. Use reflections of the triangles as reference angles to establish known values in all four quadrants of the coordinate plane.
  - **PC.FGR.3.3**: Define the six trigonometric ratios in terms of *x*, *y*, and *r* using the unit circle centered at the origin of the coordinate plane. Interpret radian measures of angles as a rotation both counterclockwise and clockwise around the unit circle.
  - **PC.FGR.3.4**: Derive the fundamental trigonometric identities.
  - **PC.FGR.3.5**: Determine the value(s) of trigonometric functions for a set of given conditions.
- Analyze trigonometric functions and their inverses.
  - **PC.FGR.3.6**: Graph and write equations of trigonometric functions using period, phase shift, and amplitude in modeling contexts.
  - **PC.FGR.3.7**: Classify the six trigonometric functions as even or odd and describe the symmetry.
  - **PC.FGR.3.8**: Restrict the domain of a trigonometric function to create an invertible function and graph the inverse function. Evaluate inverse trigonometric expressions.

## Georgia Milestones coverage

No Georgia Milestones blueprint cites this standard.

Source: Georgia Standards of Excellence, published by the Georgia Department of Education at case.georgiastandards.org.