Lesson 5: 4.5 Graphs of Sine and Cosine Functions
Duration of Days: 5
Lesson Objective
1. Sketch the graphs of basic sine and cosine functions.
2. Use amplitude and period to help sketch the graphs of sine and cosine functions.
3. Sketch translations of graphs of sine and cosine functions.
4. Use sine and cosine functions to model real-life data.
How do you sketch the graphs of sine and cosine functions?
cycle
period
amplitude
intercept
minimum
maximum
parent function
translation
transformation
vertical/horizontal shrink/stretch
phase shift
HSF-TF. B. 5 - Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
Use Khan Academy resources.
Students will graph sine and cosine functions using prior knowledge of the values of sine and cosine at different values of sine and cosine at different values of theta. These graphs will allow the students to understand the applications of sine and cosine functions in real-life problems with data that are periodic.
Sine an cosine functions are often used in scientific calculations. For instance, you can use a trigonometric function to model the percent of the moon's face that is illuminated for any given day in 2020.
Some students may incorrectly think that the amplitude of a graph is negative if a<0. Remind students that the amplitude describes a distance, which is positive.
Some students may struggle when finding the key points used for sketching. Remind students that the key points divide the interval into four parts, so they can use the average of the first and last points to find the third point, and so on.
Some students forget the starting positions of the sine and cosine functions. Remind students that f(x)=sinx passes through the origin and g(x)=cosx passes through the point (0,1).
To emphasize determining and locating key points (intercepts, minima, and maxima), have your students mark each of the points on their graphs and then check their graphs with their graphing utilities.
It may be helpful for students to understand the terms amplitude, frequency, and period using real-life contexts such as the water cycle, phases of the moon, temperatures throughout the year, and other applications in our world that are periodic.
When students are sketching the graphs of sine and cosine functions, remind them to list five key points in one period of each graph.
Use common assessments.
Pre-Calculus with Limits resources.