Florida B.E.S.T. MA.912.T.3.1
The Standard
Given a mathematical or real-world context, choose sine, cosine or tangent trigonometric functions to model periodic phenomena with specified amplitude, frequency, horizontal shift and midline.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students read a context or graph and decide whether sine, cosine, or tangent matches its shape and starting point. They build an equation using the given amplitude, frequency, horizontal shift, and midline, then interpret it in context.
What Mastery Looks Like
- A student can find the midline and amplitude from extrema and convert among frequency, period, and the input coefficient. The student writes a shifted model and checks it at key times from the context.
Common Misconceptions
- Students often use the maximum as the amplitude instead of half the range, or place the midline at zero. They may treat the input coefficient as the period, or reverse the sign of a horizontal shift. They may choose tangent for bounded data, overlooking its asymptotes and lack of a maximum or minimum.
How to Assess It
- Exit ticket: A Ferris wheel seat is 26 meters high at time zero, has a minimum height of 2 meters, and repeats every 40 seconds. Write a model and explain why sine, cosine, or tangent fits.
Lesson moves
Ways to Teach It
Use a spring, stopwatch, and motion data to record height over time, then fit a sinusoidal model and label its parameters.
Compare Ferris wheel and tide graphs, then explain in writing whether sine or cosine gives the simpler starting position.
Run a model-match card sort with context cards, parameter cards, and sine, cosine, or tangent equation cards.
Model daylight hours, alternating current, or rotating machinery from a small data table, and justify the chosen function.
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Related Standards
- MA.912.T.3.3
Solve and graph mathematical and real-world problems that are modeled with trigonometric functions. Interpret key features and determine constraints in terms of...
- MA.912.T.1
Define and use trigonometric ratios, identities or functions to solve problems.
- MA.912.T.3
Graph and apply trigonometric relations and functions.
- MA.912.T.1.8
Solve mathematical and real-world problems involving one-variable trigonometric ratios.
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