Chapter 13 Section 2
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Transcript of Chapter 13 Section 2
![Page 1: Chapter 13 Section 2](https://reader036.fdocuments.in/reader036/viewer/2022062422/56812bb7550346895d8ffa9d/html5/thumbnails/1.jpg)
Chapter 13 Section 2
Angles and the Unit circle
![Page 2: Chapter 13 Section 2](https://reader036.fdocuments.in/reader036/viewer/2022062422/56812bb7550346895d8ffa9d/html5/thumbnails/2.jpg)
• Parts of an angle
Initial Side
Terminal Side
Vertex
![Page 3: Chapter 13 Section 2](https://reader036.fdocuments.in/reader036/viewer/2022062422/56812bb7550346895d8ffa9d/html5/thumbnails/3.jpg)
Standard Position
• Vertex is at the center
• Initial side is on the + x axis
700
![Page 4: Chapter 13 Section 2](https://reader036.fdocuments.in/reader036/viewer/2022062422/56812bb7550346895d8ffa9d/html5/thumbnails/4.jpg)
Standard Position
• If terminal ray is in the II quadrant
300
![Page 5: Chapter 13 Section 2](https://reader036.fdocuments.in/reader036/viewer/2022062422/56812bb7550346895d8ffa9d/html5/thumbnails/5.jpg)
Standard Position
• If terminal side is in the III quadrant
200
![Page 6: Chapter 13 Section 2](https://reader036.fdocuments.in/reader036/viewer/2022062422/56812bb7550346895d8ffa9d/html5/thumbnails/6.jpg)
Standard Position
• If terminal side is in the IV quadrant
400
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450
110
150
Find the measure of each angle
![Page 8: Chapter 13 Section 2](https://reader036.fdocuments.in/reader036/viewer/2022062422/56812bb7550346895d8ffa9d/html5/thumbnails/8.jpg)
Negative Angle
• If you measure an angle counter clockwise you call can give the angle a negative degree
-400
![Page 9: Chapter 13 Section 2](https://reader036.fdocuments.in/reader036/viewer/2022062422/56812bb7550346895d8ffa9d/html5/thumbnails/9.jpg)
Co-Terminal measures
• A negative angle and + angle measure that describe the same angle are called Co- Terminal
-400 and 320o are co-terminal
![Page 10: Chapter 13 Section 2](https://reader036.fdocuments.in/reader036/viewer/2022062422/56812bb7550346895d8ffa9d/html5/thumbnails/10.jpg)
Find the Co Terminal Angle
• -350
• -2000
• -3000
• -2820
• 1850
• 3300
![Page 11: Chapter 13 Section 2](https://reader036.fdocuments.in/reader036/viewer/2022062422/56812bb7550346895d8ffa9d/html5/thumbnails/11.jpg)
Unit Circle
• A Circle with a radius of one unit centered on the origin
1 unit
(1,0)
![Page 12: Chapter 13 Section 2](https://reader036.fdocuments.in/reader036/viewer/2022062422/56812bb7550346895d8ffa9d/html5/thumbnails/12.jpg)
Unit CircleFor angles in standard position we use the variable
to show we are talking about an angle
1 unit
(1,0)
(
![Page 13: Chapter 13 Section 2](https://reader036.fdocuments.in/reader036/viewer/2022062422/56812bb7550346895d8ffa9d/html5/thumbnails/13.jpg)
For any point on the unit circle, we can find the coordinates by using the angle in standard position and the rule
(cos() , sin())
1 unit
(1,0)
(cos() , sin())
![Page 14: Chapter 13 Section 2](https://reader036.fdocuments.in/reader036/viewer/2022062422/56812bb7550346895d8ffa9d/html5/thumbnails/14.jpg)
Cosine and Sine of 30-60-90 triangles
1
2
3
Sin (30)
Cos (30)
![Page 15: Chapter 13 Section 2](https://reader036.fdocuments.in/reader036/viewer/2022062422/56812bb7550346895d8ffa9d/html5/thumbnails/15.jpg)
Cosine and Sine of 30-60-90 triangles
1
2
3
Sin (60)
Cos (60)
300
![Page 16: Chapter 13 Section 2](https://reader036.fdocuments.in/reader036/viewer/2022062422/56812bb7550346895d8ffa9d/html5/thumbnails/16.jpg)
Cosine and Sine of 45-45-90 triangles
1
1
2
Sin (45)
Cos (45)
450
![Page 17: Chapter 13 Section 2](https://reader036.fdocuments.in/reader036/viewer/2022062422/56812bb7550346895d8ffa9d/html5/thumbnails/17.jpg)
For angles with a terminal side not in the 1st quadrant
1 unit
(1,0)
(- , )
Make a 30-60-90 triangle and look at the coordinates
![Page 18: Chapter 13 Section 2](https://reader036.fdocuments.in/reader036/viewer/2022062422/56812bb7550346895d8ffa9d/html5/thumbnails/18.jpg)
For angles with a terminal side not in the 1st quadrant use the rule QI (+,+) QII (-,+) QIII (-,-) QIV(+,-)
1 unit
(1,0)
(- ,- )
Make a 30-60-90 triangle and look at the coordinates
![Page 19: Chapter 13 Section 2](https://reader036.fdocuments.in/reader036/viewer/2022062422/56812bb7550346895d8ffa9d/html5/thumbnails/19.jpg)
For angles with a terminal side not in the 1st quadrant use the rule QI (+,+) QII (-,+) QIII (-,-) QIV(+,-)
1 unit
(1,0)
( ,- )
U Try
![Page 20: Chapter 13 Section 2](https://reader036.fdocuments.in/reader036/viewer/2022062422/56812bb7550346895d8ffa9d/html5/thumbnails/20.jpg)
![Page 21: Chapter 13 Section 2](https://reader036.fdocuments.in/reader036/viewer/2022062422/56812bb7550346895d8ffa9d/html5/thumbnails/21.jpg)
Do Now
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