Intro to Sinusoidal Functions

DATE: 2/9/11 CLASS PERIOD: PreCalc UNIT: U.C. 2-2 .

LESSON OBJECTIVES:

Students will learn the standard form of a sine equation, y=a*sinb*x+c+d, and how each of the parameters a, b, c, and d affect the equivalent graph. This lesson corresponds to Common Core State Standards- Trigonometric Functions F-TF 2. Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. 3. Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π–x, π+x, and 2π–x in terms of their values for x, where x is any real number.

Schedule / Activities
Warmup (10’) / Knowledge Rating Scale
Lesson (20’) / Lecture. See attached notes.
Work Time (15’) / Worksheet (CPM p.20)

Unit Circle 2-2 Warm Up Name ______

KNOWLEDGE RATING SCALE

Term Know It Well Have Heard of It No Clue

Amplitude

Period

Minimum

Maximum

Domain

Range

Shift

Unit Circle 2-2 Warm Up Name ______

KNOWLEDGE RATING SCALE

Term Know It Well Have Heard of It No Clue

Amplitude

Period

Minimum

Maximum

Domain

Range

Shift

I. Features of Sinusoidal Waves

A. Sine waves and cosine waves belong to the same family. They are called “sinusoidal waves” because they have the same overall shape. Did you notice when you made these posters the similarities between sine and cosine? What are the domain and range of these guys?

B. There are certain features of these waves we need to discuss.

1. Maxima and Minima. The highest and lowest points on the graph.

Question: What is the maximum of y=sin(x)? How many are there?

Examples:

2. Period. The distance between two maxima (or minima).

Question: How do I embiggen or small the period?

Examples:

3. Amplitude. How tall the graph is. This is measured from the midline or axis. If you measure from min to max, the amplitude is half of that.

Question: How do I make it taller?

Examples:

4. Shift. Vertical and horizontal.

Question: How do I move it up/down or left/right? [LARS]

Examples:

II. Other Questions

è How do I move it up or down?

è What if I wanted min at zero instead of -1?

è What if I wanted to start at π4 radians instead of 0 or π2?

è What if my curve looked like this? (A=2 or period=4)

III. Formalize

y=a*sinbx+c+d

IV. Examples and close

V. Homework (CPM p. 20)