This is the first of two lessons focused on students identifying important features of trigonometric functions when starting from equations or graphs. They also examine how a horizontal scale factor affects the period of these types of functions.  

The Warm-up introduces students to what cosine and sine functions with different periods can look like. In a later activity, they focus on and use different representations to make sense of why the graph of this function appears horizontally compressed compared to the graph of .

Students make use of structure when they work on the matching task, as they identify important structural properties of graphs and equations (MP7). These properties include midline, amplitude, and horizontal translations, and students need to identify these aspects of a function both from the expression defining the function and from its graph.

Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.