CCSS.Math.Content.HSF-TF.B

CCSS.Math.Content.HSF-TF.B is a cluster heading. These are the individual standards under it.

• 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.B.6

  (+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.

• 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...

01

What Students Need to Do

Students represent repeating patterns with sine or cosine functions. They identify amplitude, period, frequency, midline, and phase shift, then use the model to make predictions.

02

What Mastery Looks Like

Given a graph, table, or context, students can write a sine or cosine equation with correct parameters. They can use the equation to predict values and explain what each parameter means.

03

Common Misconceptions

Students often call the maximum value the amplitude instead of finding half the range. They may confuse period with frequency, reverse a phase shift’s sign, or mix degrees and radians.

04

How to Assess It

Exit ticket: A rider’s height ranges from 2 to 18 meters and repeats every 40 seconds, starting at minimum. Write a model and find the height at 10 seconds.

1. 01

   Rotate a marked paper plate beside a ruler, record the point’s height every 15 degrees, and graph the ordered pairs.

2. 02

   Ask students to explain whether sine or cosine better models a Ferris wheel rider starting at the bottom.

3. 03

   Play parameter match: teams pair sine and cosine equations with graph cards showing different amplitudes, periods, midlines, and shifts.

4. 04

   Use monthly daylight data for your city to build a sinusoidal model and predict daylight hours for an unlisted date.

• 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.A.4

  (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.