Specific Expectations
2.4 sketch the graphs of f(x) =sinx and f(x) =cosx for angle measures expressed in degrees, and determine and describe their key properties
2.6 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
2.7 sketch graphs of y = af (k(x – d)) + c by applying one or more transformations to the graphs of f(x) =sinx and f(x) =cosx, and state the domain and range of the transformed functions
2.8 represent a sinusoidal function with an equation, given its graph or its properties Sample problem: A sinusoidal function has an amplitude of 2 units, a period of 180º, and a maximum at (0, 3). Represent the function with an equation in two different ways.
Materials
Pencil, graph paper, cards with starter problems
Important Terminology
domain, range, amplitude, period, phase shift.
Background Knowledge
Hook
Lesson Sequence
Break the class up into groups of 3. Distribute problem cards. Each student in the group picks a card. Each card will have either a graph, a function, or a list of properites. Each student takes whichever card they are given, and creates the missing two cards. They then pass the cards to their group mates, who repeat the process. They then compare their answers. Repeat once more, then have the students make up their own problem cards. Return the original card. This leaves 3 pair of cards showing the same function. Have the students from groups of 6, and assemble 3 decks of cards, each deck containing 1 pair from each function, but not identical, i.e. one pair can consist of a graph card and an equation card. Keep 1 deck, pass one to the group to your right, and one to the group on your left. Play go fish with the cards.
Key Questions
Leading questions given by you to the students and expected questions from the students
Assessment
Students can do a self assessment or mark each others work.
Enrichment
Remediation
Implications for Future Lessons