Thursday, March 26, 2009
Intro to Calculus (Class 66)
Announcements
Test next Friday (150 points) covering logs to sinusoidals. It will take the entire block.
Lesson Title
Circular Functions (19)
Overview
The opener for today focuses students on how to stretch or compress a sinusoidal function in order to force it to have the period desired. The remaining class will be focused on developing the skills needed to create sinusoidal functions to model periodic relationships.
Textbook Sections
N/A
Vocabulary
radian
central angle
terminal side
circumference
rotation
circular function
sine
cosine
tangent
cosecant
secant
cotangent
Key Attitudes
Math is about using what you know to create something new.
Key Ideas
A point rotating on the circumference of a circle can be used to generate a sine or cosine graph by plotting the height of the sine (or cosine) as a function of the measure of the central angle.
Graphs of sinusoidal functions can be stretched, compressed, shifted, and reflected in the same way that graphs of any function can.
A point rotating on the circumference of a circle can be used to generate a sine or cosine graph by plotting the height of the sine (or cosine) as a function of time when the point of on the circumference of the circle is rotating at some speed.
Increasing the speed at which the point on the circumference of a circle is rotating makes the graph of the sine or cosine have more “bump” in a given time. In other words, increasing the rotation speed shortens the period of the function. Decreasing the speed, increases the period.
Key Skills
I can determine the transformations needed to change the graph of one function into another.
I can deduce the necessary graphical translations needed to change the graph of a sine or cosine function into a graph which will accurately represent a situation.
Turn-In (#65)
Homework 21 #1-6
Handouts
Homework 21
Assignment
Homework 21 #7-12
Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word.
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