The document covers the properties and functions of sine and cosine, including their graphs, periods, amplitudes, and the relationship with the unit circle. It features activities and bellringers for practicing key concepts, as well as a creed emphasizing the importance of mastering the unit circle in understanding trigonometry. Additionally, it provides resources for further exploration of the topic.

1. THE SINE FUNCTION
AND
THE COSINE FUNCTION
Chapter 13:
Periodic
Functions and
Trigonometr y
pp. 734-748

2. BELLRINGERS
Use the graph. Find the value of the following.
1.The period
A.2
B.4
C. 6
D.8

3. BELLRINGERS
Use the graph. Find the value of the following.
2. The domain
A. All real numbers
between -1 and 1,
inclusively
B. All real numbers
greater than zero
C. All real numbers
D. None of the above

4. BELLRINGERS
Use the graph. Find the value of the following.
3. The amplitude
A.1
B.2
C. 3
D.4

5. BELLRINGERS
Use the graph. Find the value of the following.
4.The range
A. All real numbers
between -1 and
1, inclusively
B. All real numbers
greater than
zero
C. All real numbers
D. None of the
above

6. BELLRINGERS
Fill the x-coordinate of each point on the
Unit Circle.
1. A
A.
B.
C.
D.
2. B
A.
B.
C.
D.
-1
0
½
1
3. C
A.
B.
C.
D.
-1
0
½
1
-1
0
½
1
4. D
A.
B.
C.
D.
-1
0
½
1

7. UNIT CIRCLE WORKSHEET
The Unit Circle’s Creed
This is my U nit Circle. There are many like it, but this one is mine.
My Unit Circle is my best friend. It is my life. I must master it as I must
master my life.
My Unit Circle, without me, is still useful, but without my Unit Circle, I am
useless. I must utilize my Unit Circle true. I must conver t my degrees into
radians and vice ver sa. I must recognize how special right triangles play
a vital role in using my Unit Circle. I will...
My Unit Circle and I know that what counts in this algebra class is not the
rounds we fire, the noise of our bur st, nor the smoke we make. We know
that it is the understanding that counts. We will under stand...
My Unit Circle is human, even as I, because it is my life. Thus, I will learn
it as a brother. I will learn its degrees, its radians, its coordinates, its
proper ties, its relationships and its purpose. I will keep my Unit Circle
clean and ready, even as I am clean and ready. We will become par t of
each other. We will...
Before all that is holy, I swear this creed. My Unit Circle and I are the
defenders of mathematics. We are the masters of misconceptions. We
are the saviors of understanding.
So be it, until victor y is Mathematics' and there are no misconceptions,
but under standing!

8. SINE/COSINE POSTER BOARD ACTIVIT Y
Notable Board Contents :
 Definition (in terms of function and graph)
 Graph
 Proper ties
 Period
 Amplitude
 Relationships
 Functions
 Degrees and radians
 Unit Circle…
 Anything else you can find in 14 minutes that will help you present
your board

9. THE RELATIONSHIP BETWEEN THE UNIT
CIRCLE AND SINE/COSINE FUNCTIONS
 Links that explore the relationship
http://www.mathsisfun.com/algebra/trig-interactive-unit-circle.html
http://www.mathsisfun.com/geometry/unit-circle.html
http://www.absorblearning.com/media/attachment.action?quick=je
&att=1388
http://curvebank.calstatela.edu/unit/unit.htm

10. NOTABLE TERMS
From this lesson…
 Sine function
 Sine curve
 Cosine function
You should know the following, but make note…
 Period
 Cycle
 Amplitude
 Unit circle
 Cosine of θ
 Sine of θ
 Radian

11. THE UNIT CIRCLE AND SINE

12. INTERPRETING THE SINE FUNCTION IN
DEGREES

13. ESTIMATING SINE VALUES IN RADIANS

14. FINDING THE PERIOD OF A SINE
FUNCTION

15. FINDING THE AMPLITUDE OF A SINE
CURVE

16. SKETCHING A GRAPH OF THE SINE
FUNCTION

17. “GRAPHING FROM A FUNCTION” RULE

18. FINDING THE PERIOD AND WRITING AND
EQUATION WITH IT

19. THE UNIT CIRCLE AND COSINE

20. INTERPRETING THE GRAPH OF COS Θ

21. SKETCHING THE GRAPH OF A COSINE
FUNCTION

22. SOLVING A COSINE EQUATION