Sine and Cosine Functions Ppt
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Transcript of Sine and Cosine Functions Ppt
![Page 1: Sine and Cosine Functions Ppt](https://reader033.fdocuments.us/reader033/viewer/2022061207/54840daab4af9fbd5d8b460c/html5/thumbnails/1.jpg)
Chapter 13:Periodic Functions and Trigonometry
pp. 734-748
THE SINE FUNCTIONAND
THE COSINE FUNCTION
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1.The period
A.2B.4C.6D.8
BELLRINGERS
Use the graph. Find the value of the following.
![Page 3: Sine and Cosine Functions Ppt](https://reader033.fdocuments.us/reader033/viewer/2022061207/54840daab4af9fbd5d8b460c/html5/thumbnails/3.jpg)
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.
![Page 4: Sine and Cosine Functions Ppt](https://reader033.fdocuments.us/reader033/viewer/2022061207/54840daab4af9fbd5d8b460c/html5/thumbnails/4.jpg)
3. The amplitude
A.1B.2C.3D.4
BELLRINGERS
Use the graph. Find the value of the following.
![Page 5: Sine and Cosine Functions Ppt](https://reader033.fdocuments.us/reader033/viewer/2022061207/54840daab4af9fbd5d8b460c/html5/thumbnails/5.jpg)
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.
![Page 6: Sine and Cosine Functions Ppt](https://reader033.fdocuments.us/reader033/viewer/2022061207/54840daab4af9fbd5d8b460c/html5/thumbnails/6.jpg)
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.
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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
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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
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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
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From this lesson…Sine functionSine curveCosine function
You should know the following, but make note…PeriodCycleAmplitudeUnit circleCosine of θSine of θRadian
NOTABLE TERMS
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THE UNIT CIRCLE AND SINE
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INTERPRETING THE SINE FUNCTION IN DEGREES
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ESTIMATING SINE VALUES IN RADIANS
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FINDING THE PERIOD OF A SINE FUNCTION
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FINDING THE AMPLITUDE OF A SINE CURVE
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SKETCHING A GRAPH OF THE SINE FUNCTION
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“GRAPHING FROM A FUNCTION” RULE
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FINDING THE PERIOD AND WRITING AND EQUATION WITH IT
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THE UNIT CIRCLE AND COSINE
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INTERPRETING THE GRAPH OF COS Θ
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SKETCHING THE GRAPH OF A COSINE FUNCTION
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SOLVING A COSINE EQUATION