CCSS.Math.Content.HSF-TF.B.5
The standard
Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
Common Core State Standards for Mathematics
What this standard means
Students need to match a sine or cosine function to a repeating situation. They should identify the midline, amplitude, and frequency or period from a graph, table, description, or data set, then build a model that fits those features.
Mastery looks like writing a function such as y = A sin(Bx) + D or y = A cos(Bx) + D and explaining what each number means in context. Students often mix up amplitude with maximum value, frequency with period, or forget that the midline shifts the whole graph up or down.
Ways to teach it
- Use a Ferris wheel height graph and have students label maximum, minimum, midline, amplitude, and period with colored pencils.
- Ask students: How would you model daily temperature if the high is 82, low is 58, and the cycle repeats every 24 hours?
- Give one graph and ask students to write A, B, D, period, and a possible sine or cosine equation on an exit ticket.
- Show a tide chart from a local beach and have students estimate a trig model for water height over time.
Plan a lesson for CCSS.Math.Content.HSF-TF.B.5
Generate a complete lesson plan aligned to this standard, with objectives, activities, and materials. Free, no account needed.
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.B
Model periodic phenomena with trigonometric functions
- CCSS.Math.Content.HSF-TF.B.7
(+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms...
- CCSS.Math.Content.HSF-TF.A.4
(+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.