NY Next Generation Math AII-F.TF.5
The Standard
Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, horizontal shift, and midline.
New York State Next Generation Mathematics Learning Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students choose sine or cosine to model periodic data and set amplitude, frequency, horizontal shift, and midline. They explain how each parameter matches the phenomenon.
What Mastery Looks Like
- The student builds a sinusoidal model from a graph or data set and checks key points. The stated amplitude, period, shift, and midline agree with the context.
Common Misconceptions
- Students may confuse frequency with period or use the maximum as the amplitude. They may shift the graph in the wrong direction or omit the midline.
How to Assess It
- Give one cycle of periodic data with a maximum, minimum, and timing information. Ask students to write and interpret a sine or cosine model.
Lesson moves
Ways to Teach It
Stretch string over a plotted cycle, then mark amplitude, period, phase shift, and midline with labels.
Ask whether sine or cosine gives a simpler model for data beginning at a maximum.
Play parameter match by pairing sinusoidal equations with shifted and scaled graph cards.
Model daylight hours, tides, or a Ferris wheel height over time.
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Printable AII-F.TF.5 Worksheet
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Related Standards
- AII-F.TF.4
Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
- AII-F.IF.7.e
Graph cube root, exponential and logarithmic functions, showing intercepts and end behavior; and trigonometric functions, showing period, midline, and amplitude...
- AI-F.LE.1
Distinguish between situations that can be modeled with linear functions and with exponential functions.
- AII-F.TF.2
Apply concepts of the unit circle in the coordinate plane to calculate the values of the six trigonometric functions given angles in radian measure.
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