HolcombMath

Wednesday, February 18, 2009

Intro to Calculus (Class 53)

Lesson Title
Circular Functions (6)

Overview
Students begin the class today by working to finish Sangaku 11. They then can continue their work on Workshop 16. We will then have a lesson to “level up” on circular functions by connecting what we have been working on to two old friends.
Textbook Sections
N/A

Vocabulary
radian
central angle
terminal side
circumference
rotation
circular function

Key Attitudes
Math is about using what you know to create something new.

Key Ideas
Given two points on the circumference of a circle, one of the points can be rotated around the center to match up with the other point in an infinite number of ways.
The location of the point of intersection of the terminal side of a central angle and a circle are related to each other. This relationship is what is meant by the term “circular function”.
The sine of a central angle in the unit circle is defined as the y-coordinate of the point of intersection of the terminal side of the angle and the unit circle.
The cosine of a central angle in the unit circle is defined as the y-coordinate of the point of intersection of the terminal side of the angle and the unit circle.
Key Skills
I can explain what a radian is.
I can give a mathematical reason for why radians are “better” than degrees.
I can find the location of a point on the circumference of a circle resulting from a rotation about the center of the circle using radians.
I can determine the quadrant that a point on the circumference of a circle will end up in as the result of a rotation about the center given in radian.
I can determine the measure of coterminal angles.
If I know the location of the point of intersection of the terminal side of an angle, then I can find the location of the point of intersection of the terminal side of “family members” of this angle by thinking geometrically.
I can translate between what I have learned about circular functions and the definition of the sine and the cosine of a central angle.
Turn-In (#52)
Finish Workshop 15
Workshop 16 #1,2

Handouts
Homework 18

Assignment
Snagaku 11
Workshop 16
Homework 18 #TBA
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.