Chapter 13:Periodic Functions and Trigonometry

pp. 734-748

THE SINE FUNCTIONAND

THE COSINE FUNCTION

1.The period

A.2B.4C.6D.8

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 numbersD.None of the

above

BELLRINGERS

Use the graph. Find the value of the following.

3. The amplitude

A.1B.2C.3D.4

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 numbersD.None of the

above

BELLRINGERS

Use the graph. Find the value of the following.

1. AA. -1B. 0C. ½D. 1

2. BA. -1B. 0C. ½D. 1

3. CA. -1B. 0C. ½D. 1

4. DA. -1B. 0C. ½D. 1

BELLRINGERS

Fill the x-coordinate of each point on the Unit Circle.

This is my Unit Circle. There are many l ike it, but this one is mine.My Unit Circle is my best fr iend. It is my l i fe. I must master it as I must master my l i fe.My Unit Circle, without me, is sti l l useful, but without my Unit Circle, I am useless. I must uti l ize my Unit Circle true. I must convert my degrees into radians and vice versa. I must recognize how special r ight tr iangles play a vital role in using my Unit Circle. I wi l l . . .My Unit Circle and I know that what counts in this algebra class is not the rounds we fi re, the noise of our burst, nor the smoke we make. We know that it is the understanding that counts. We wil l understand...My Unit Circle is human, even as I , because it is my l i fe. Thus, I wi l l learn it as a brother. I wi l l learn its degrees, its radians, its coordinates, its properties, i ts relationships and its purpose. I wi l l keep my Unit Circle clean and ready, even as I am clean and ready. We wil l become part of each other. We wil l . . .Before al l 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, unti l victory is Mathematics' and there are no misconceptions, but understanding!

UNIT CIRCLE WORKSHEET

The Unit Circle’s Creed

Notable Board Contents:

Defi nition (in terms of function and graph) Graph Properties

PeriodAmplitudeRelationshipsFunctionsDegrees and radians

Unit Circle… Anything else you can fi nd in 14 minutes that will help you

present your board

SINE/COSINE POSTER BOARD ACTIVITY

THE RELATIONSHIP BETWEEN THE UNIT CIRCLE AND SINE/COSINE

FUNCTIONSLinks 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

From this lesson…Sine functionSine curveCosine function

You should know the following, but make note…PeriodCycleAmplitudeUnit circleCosine of θSine of θRadian

NOTABLE TERMS

THE UNIT CIRCLE AND SINE

INTERPRETING THE SINE FUNCTION IN DEGREES

ESTIMATING SINE VALUES IN RADIANS

FINDING THE PERIOD OF A SINE FUNCTION

FINDING THE AMPLITUDE OF A SINE CURVE

SKETCHING A GRAPH OF THE SINE FUNCTION

“GRAPHING FROM A FUNCTION” RULE

FINDING THE PERIOD AND WRITING AND EQUATION WITH IT

THE UNIT CIRCLE AND COSINE

INTERPRETING THE GRAPH OF COS Θ

SKETCHING THE GRAPH OF A COSINE FUNCTION

SOLVING A COSINE EQUATION