PC.FGR.3Trigonometric Modeling Overview

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.