Chapter 4: Circular Functions Lesson 7: Scale-Change Images to Trig Functions Mrs. Parziale.
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Transcript of Chapter 4: Circular Functions Lesson 7: Scale-Change Images to Trig Functions Mrs. Parziale.
![Page 1: Chapter 4: Circular Functions Lesson 7: Scale-Change Images to Trig Functions Mrs. Parziale.](https://reader036.fdocuments.net/reader036/viewer/2022082505/56649d0e5503460f949e4155/html5/thumbnails/1.jpg)
Chapter 4: Circular Functions
Lesson 7: Scale-Change Images to Trig Functions
Mrs. Parziale
![Page 2: Chapter 4: Circular Functions Lesson 7: Scale-Change Images to Trig Functions Mrs. Parziale.](https://reader036.fdocuments.net/reader036/viewer/2022082505/56649d0e5503460f949e4155/html5/thumbnails/2.jpg)
• Parent Sine or Cosine Function:
• General form of Sine or Cosine Function: siny x cosy x
siny a bx cosy a bx
![Page 3: Chapter 4: Circular Functions Lesson 7: Scale-Change Images to Trig Functions Mrs. Parziale.](https://reader036.fdocuments.net/reader036/viewer/2022082505/56649d0e5503460f949e4155/html5/thumbnails/3.jpg)
Example 1:
• Using your TI83, Graph and Compare the following functions.
• How do these two graphs compare?– What are their maximum points?– What are their minimum points?– What relationship do you see with the equation?– What is the amplitude?
sin 3siny x y x
2 4 4x y
a
![Page 4: Chapter 4: Circular Functions Lesson 7: Scale-Change Images to Trig Functions Mrs. Parziale.](https://reader036.fdocuments.net/reader036/viewer/2022082505/56649d0e5503460f949e4155/html5/thumbnails/4.jpg)
What’s the Amplitude?
• What is the amplitude of the following equations?
• a)
• b)
• c)
4siny x1sin2
y x
2siny x
![Page 5: Chapter 4: Circular Functions Lesson 7: Scale-Change Images to Trig Functions Mrs. Parziale.](https://reader036.fdocuments.net/reader036/viewer/2022082505/56649d0e5503460f949e4155/html5/thumbnails/5.jpg)
Example 2:
• Using your TI83, Graph and Compare the following functions.
• Describe how the two graph are different.– What is the value of the maximum?– What is the value of the minimum?– How many cycles of the sine curve are there on each
graph from 0 to 2?– What is the Period?
sin sin 2y x y x
2
b
![Page 6: Chapter 4: Circular Functions Lesson 7: Scale-Change Images to Trig Functions Mrs. Parziale.](https://reader036.fdocuments.net/reader036/viewer/2022082505/56649d0e5503460f949e4155/html5/thumbnails/6.jpg)
How Many Cycles?
• How many cycles of the sine curve are on the graphs for the equations below?
a)
b)
c)
sin 3y x
1sin2
y x
sin 4y x
![Page 7: Chapter 4: Circular Functions Lesson 7: Scale-Change Images to Trig Functions Mrs. Parziale.](https://reader036.fdocuments.net/reader036/viewer/2022082505/56649d0e5503460f949e4155/html5/thumbnails/7.jpg)
Example 3:
• Identify the amplitude and period for the following sine functions.
5siny xamplitude: ____
period: _______
sin 4y x
amplitude: ____
period: _______
![Page 8: Chapter 4: Circular Functions Lesson 7: Scale-Change Images to Trig Functions Mrs. Parziale.](https://reader036.fdocuments.net/reader036/viewer/2022082505/56649d0e5503460f949e4155/html5/thumbnails/8.jpg)
Example 3, cont.:
• Identify the amplitude and period for the following sine functions.
amplitude: ____
period: _______
3sin 2y x
![Page 9: Chapter 4: Circular Functions Lesson 7: Scale-Change Images to Trig Functions Mrs. Parziale.](https://reader036.fdocuments.net/reader036/viewer/2022082505/56649d0e5503460f949e4155/html5/thumbnails/9.jpg)
Graphing Sine and Cosine Functions:
• To graph the sine and cosine functions, you need five key points which include the x- and y-intercepts and the maximum and minimum points. Take the following steps when graphing the sine and cosine functions.
• Step 1: Find the amplitude and period of the function.• Step 2: Divide the section of the graph into four equal
parts.• Step 3: Find the intercept points.• Step 4: Find the max and min points.• Step 5: Graph the five points and draw a smooth curve
through them.
![Page 10: Chapter 4: Circular Functions Lesson 7: Scale-Change Images to Trig Functions Mrs. Parziale.](https://reader036.fdocuments.net/reader036/viewer/2022082505/56649d0e5503460f949e4155/html5/thumbnails/10.jpg)
Example 4:
• Graph • Amplitude = ________• Period = __________• x-intercepts = ______, _____, • y-intercept = ______• max = _________ • min = _________
sin 4y x
![Page 11: Chapter 4: Circular Functions Lesson 7: Scale-Change Images to Trig Functions Mrs. Parziale.](https://reader036.fdocuments.net/reader036/viewer/2022082505/56649d0e5503460f949e4155/html5/thumbnails/11.jpg)
Example 5:
• Graph • Amplitude = ________• Period = __________• x-intercepts = ______, _____, • y-intercept = ______• max = _________ • min = _________
3sin 2y x
![Page 12: Chapter 4: Circular Functions Lesson 7: Scale-Change Images to Trig Functions Mrs. Parziale.](https://reader036.fdocuments.net/reader036/viewer/2022082505/56649d0e5503460f949e4155/html5/thumbnails/12.jpg)
Example 6:
• Graph • Amplitude = ________• Period = __________• x-intercepts = ______, _____, • y-intercept = ______• max = _________ • min = _________
cos 2y x
![Page 13: Chapter 4: Circular Functions Lesson 7: Scale-Change Images to Trig Functions Mrs. Parziale.](https://reader036.fdocuments.net/reader036/viewer/2022082505/56649d0e5503460f949e4155/html5/thumbnails/13.jpg)
Example 7:
• Graph • Amplitude = ________• Period = __________• x-intercepts = ______, _____, • y-intercept = ______• max = _________ • min = _________
.25sin 4y x
![Page 14: Chapter 4: Circular Functions Lesson 7: Scale-Change Images to Trig Functions Mrs. Parziale.](https://reader036.fdocuments.net/reader036/viewer/2022082505/56649d0e5503460f949e4155/html5/thumbnails/14.jpg)
Graphing the Tangent Function
• The parent tangent function has a period of . When graphing the tangent function, you will need to know the x-intercept, vertical asymptotes, the halfway points, and the period.
• Period = ___________ • Vertical asymptotes are defined at odd
multiples of ______________
![Page 15: Chapter 4: Circular Functions Lesson 7: Scale-Change Images to Trig Functions Mrs. Parziale.](https://reader036.fdocuments.net/reader036/viewer/2022082505/56649d0e5503460f949e4155/html5/thumbnails/15.jpg)
Example 8:
• Graph .• Period = _______ • x-intercept = _______• Vertical
Asymptotes = ________
• Halfway points = ___, ___
3tan 2y x
![Page 16: Chapter 4: Circular Functions Lesson 7: Scale-Change Images to Trig Functions Mrs. Parziale.](https://reader036.fdocuments.net/reader036/viewer/2022082505/56649d0e5503460f949e4155/html5/thumbnails/16.jpg)
Closure
• Given the equation• What is the amplitude?• Explain how an amplitude of ½ affects the
graph compared to the parent function?• How many cycles appear within 2π?• What is the period of the curve?• How does a period of affect the
graph?
1sin32
y x
2
3