CCSS.Math.Content.HSF-TF.B
The standard
Model periodic phenomena with trigonometric functions
Common Core State Standards for Mathematics · High School — Functions
What this standard means
Students need to use sine, cosine, or tangent to represent repeating situations. They should identify period, amplitude, midline, and phase shift from a context, table, graph, or equation. They also need to choose a reasonable model and explain what each part means.
Mastery looks like building a trig function from real data, graphing it, and using it to make predictions. Students often mix up amplitude and maximum value, use degrees and radians inconsistently, or miss the midline when the data does not center on zero.
Ways to teach it
- Hands-on activity: Use a ruler and string to model a rotating point, then record height values every 30 degrees and graph them.
- Discussion or writing prompt: Explain how you would model daylight hours over a year using a sine or cosine function.
- Quick assessment: Give a graph of tides and ask students to label amplitude, period, midline, maximum, and minimum.
- Real-world connection: Use local sunrise data for one year and have students write a trig model for daylight length.
Plan a lesson for CCSS.Math.Content.HSF-TF.B
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Related standards
- CCSS.Math.Content.HSF-IF.C.7e
Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
- CCSS.Math.Content.HSF-TF.A
Extend the domain of trigonometric functions using the unit circle
- CCSS.Math.Content.HSF-TF.B.5
Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
- CCSS.Math.Content.HSF-TF.A.4
(+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.