Mississippi Math A3.G.41

MathGrades 9–12Geometry (G) Recognize, Sketch, and Transform Graphs to Functions

The Standard

Relate symmetry of the behavior of even and odd functions.

2025 Mississippi College- and Career-Readiness Standards for Mathematics · Prove and Apply Trigonometric Identities

Teacher's field guide

What Students Need to Do: Students compare the points at x and -x on a graph. They decide whether the outputs stay the same or change sign. They use that pattern to describe symmetry in sine and cosine graphs.
What Mastery Looks Like: A student can tell whether a graph or table shows an even function, an odd function, or neither. They can explain why cosine has y-axis symmetry and sine has origin symmetry, then use that to find values at negative angles.
Common Misconceptions: Students may call any graph that crosses the origin odd. They may also confuse a reflection across the y-axis with a half-turn around the origin, or think every function must be even or odd.
How to Assess It: Exit ticket: Plot the points at x = π/6 and x = -π/6 for sine and cosine. Label each function even or odd, and write an equation that shows why.

Lesson moves

Print sine and cosine curves on tracing paper; fold each across the y-axis, then rotate it 180 degrees to see which position matches.
Ask students to compare sine and cosine at π/3 and -π/3, then explain the different patterns they find.
Give pairs of input-output cards for sine, cosine, and sine plus one; sort them by y-axis symmetry, origin symmetry, or neither.
Plot a tuning fork's sound pressure modeled by y = sin t, then compare readings at equal times before and after t = 0.

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