Circular And Periodic Functions Lesson Plan for 10th Grade Example Students

Topic: Circular and Periodic Functions

Objectives & Outcomes

• At the end of this lesson, students will be able to define circular and periodic functions, describe the characteristics of circular and periodic functions, and identify and solve problems involving circular and periodic functions.

Materials

• Whiteboard and markers
• Handouts with examples of circular and periodic functions

Warm-up

• Review the concept of linear functions and ask students to give examples of linear functions.
• Next, ask students to consider the graph of a linear function and consider what would happen if the graph was rotated around the origin. Would the function still be linear?
• Write the following equations on the board: y = x, y = x + 1, y = x + 2, y = x + 3. Ask students if they notice any patterns in the graphs.
• Have students try to come up with an equation that will create a graph that is a rotation of y = x + 3. (e.g. y = x - 3, y = x + 3 + 3, y = x + 6, y = x + 9)

Direct Instruction

• Introduce the concept of circular functions and explain that a function is circular if it is a rotation of another function.
• Show students the equations that students came up with and explain how they are rotations of y = x + 3.
• Next, introduce the concept of periodic functions and explain that a function is periodic if it has a period, which is a number that the function repeats after a certain number of values.
• For example, the function y = x has a period of 1, since it repeats after every x value. The function y = x + 3 has a period of 3, since it repeats after every 3 values.
• Write the following functions on the board: y = x + 3, y = x + 6, y = x + 9. Ask students if they can identify the period of each function.

Guided Practice:

• Have students work in pairs to find the period of the following functions: y = x^2, y = x^3, y = x^4
• Have students share their answers with the class and explain their reasoning.
• Explain that the period of each function is because the function repeats after every x value.

Independent Practice:

• Have students work in groups to find the period of the following functions: y = sin(x), y = cos(x), y = tan(x), y = csc(x), y = sec(x), y = cot(x), y = cotan(x), y = secant(x), y = cosecant(x), y - =cotan(x), y = cosecant(x), y = secant(x), y = csc(x), y = cot(x), y = cos(x), y = tan(x), y = sin(x), y = x^3
• Have each group present their findings to the class and explain their reasoning.

Closure

• Review the concept of period and its relationship to the independent variable and the dependent variable.
• Ask students to share their favorite examples of circular and periodic functions.

Assessment

• Collect the students' worksheets and examine their understanding of circular and periodic functions through the examples they chose to solve and their solutions.
• Ask students to explain their solutions and evaluate their understanding of the concept.