Trigonometric Functions Grade 11 Functions Trigonometric Functions

Agenda Learning Goals Warm-Up Activity Note Group Activity Ticket Out the Door

Specific Expectations Determine, through investigation using technology, the roles of the parameters a,k,d and c in functions of the form y=a f(k(x-d)) + c, where f(x) = sin x or f(x) = cos x with angles expressed in degrees, and describe these roles in terms of transformations on the graphs of f(x) = sin x and f(x) = cos x Determine the amplitude, period, phase shift, domain and range of sinusoidal functions whose equations are given in the form f(x) = asin(k(x-d)) + c or f(x) = acos(k(x-d)) + c

Learning Goals Students will explain the terms domain, range, period and amplitude in terms of a sine and cosine functions. Students will differentiate between the parameters a, k, d and c and the effect they have on a sine or cosine graph

Previous Knowledge Simple knowledge of sine and cosine functions, f(x) = sin x and f(x) = cos x What the similarities and differences are between sine and cosine functions and what their graphs look like. Graphing sine and cosine functions in both radians and degrees

Warm-Up Activity Divide the class into 4 even and predetermined groups. Each group is given one of the following terms: Amplitude, Period, Domain or Range The students in each group will become experts of this term (e.g. what this word means to them, how it relates to math, real world applications, etc.)

Warm-Up Activity The students will have a KWL Chart and they will be required to fill in the first two columns during this activity. Each group of students will then present their findings to the class After each group explains their term, the teacher will reiterate what the students have said and give a visual representation of the defined term TOTAL ACTIVITY SHOULD TAKE AROUND 20 MINUTES

Content Before starting the next activity, the parameters (a, k, d & c) used for both sine and cosine functions will be presented and how they relate to the terms students just defined. These terms will be written on the board so that the students can copy them in to their notebooks to being a new note. As you go through these steps show the visual change/representation of our the graph.

Content Start with f(x) = sin x and add in the new parameters Example: Sine function will be written on the board (e.g. 2sin(x+30) - 3) Ask students to state the general equation for sine [f(x) = a sin(k(x-d))+c] and to relate it to the example. “The number 2 would affect the amplitude of our graph. The parameter causes our graph to either stretch or shrink vertically. So in this case our amplitude (distance from the axis to max or min) will be 2. Which variable in our general equation does this relate too?” 20 min

Class Activity A Jigsaw activity will then be used to move students from their previous expert groups. These will be groups of 4, containing one “expert” for each team. Each group with be given a set of 4 functions; 2 represented by an equation and 2 represented by a graph. The students will each be assigned a new parameter to be the ‘expert’ on and will need to figure out what value in their equations or graphs represent their parameter.

Class Activity Once in the ‘expert’ groups, students will be able to ask their peers for help if needed. There will also be an IPad set up at every station for students to use the Desmo App throughout the activity. Students will work on all of their assigned problems until the allotted time is up. Once the time is up, they will return to their groups and share their findings to piece together the equations and transformations of their assigned functions. The students will then hand in their worksheet. 10 min

Ticket Out the Door Ask the students if there were any questions about their assigned functions. If there are questions, use the Desmos App to demonstrate to the class how to solve them. If there are no questions, move on to the final component of the lesson.

Ticket Out the Door Have an equation on the board such as f(x) = 7 sin(0.5(x))+3 On the back of their KWL chart, tell students to sketch this function as well as g(x)=sin(x). Then, explain how the parameters have changed the graph using the Desmo application. If the students are unable to graph the function, then they are to just explain the parameters. If they are still unable to do this, then they should explain what part of the problem they are having trouble with and any questions they still have.