Section 13.6a The Unit Circle. The Unit Circle (like any circle) contains 360 ° It’s called the...
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Transcript of Section 13.6a The Unit Circle. The Unit Circle (like any circle) contains 360 ° It’s called the...
![Page 1: Section 13.6a The Unit Circle. The Unit Circle (like any circle) contains 360 ° It’s called the Unit Circle because the length of the radius is 1 π/2.](https://reader035.fdocuments.us/reader035/viewer/2022062718/56649ea85503460f94babe16/html5/thumbnails/1.jpg)
Section 13.6a
The Unit Circle
![Page 2: Section 13.6a The Unit Circle. The Unit Circle (like any circle) contains 360 ° It’s called the Unit Circle because the length of the radius is 1 π/2.](https://reader035.fdocuments.us/reader035/viewer/2022062718/56649ea85503460f94babe16/html5/thumbnails/2.jpg)
The Unit Circle (like any circle) contains 360°
It’s called the Unit Circle because the length ofthe radius is 1
π/2
r = 1
Positive angle of rotation is counter clock-wise
Positive angle of rotation is counter clock-wise
π
![Page 3: Section 13.6a The Unit Circle. The Unit Circle (like any circle) contains 360 ° It’s called the Unit Circle because the length of the radius is 1 π/2.](https://reader035.fdocuments.us/reader035/viewer/2022062718/56649ea85503460f94babe16/html5/thumbnails/3.jpg)
The Unit Circle
x
y
1
x
y(1, 0)
1
ysin
((opposite)/(hypotenuse)((opposite)/(hypotenuse)
1
xcos
(adjacent) / (hypotenuse))(adjacent) / (hypotenuse))
Therefore, the coordinates of any point on the circle are: (cos , sin )Therefore, the coordinates of any point on the circle are: (cos , sin )
sin,cosP
![Page 4: Section 13.6a The Unit Circle. The Unit Circle (like any circle) contains 360 ° It’s called the Unit Circle because the length of the radius is 1 π/2.](https://reader035.fdocuments.us/reader035/viewer/2022062718/56649ea85503460f94babe16/html5/thumbnails/4.jpg)
Values of the Unit Circle
30o
r = 1sin 30o =
2
1,
2
3
cos 30o =
3
2
1
2
![Page 5: Section 13.6a The Unit Circle. The Unit Circle (like any circle) contains 360 ° It’s called the Unit Circle because the length of the radius is 1 π/2.](https://reader035.fdocuments.us/reader035/viewer/2022062718/56649ea85503460f94babe16/html5/thumbnails/5.jpg)
Values of the Unit Circle
45o
r = 1sin 45o =
cos 45o =
2
2,
2
2
2
2
2
2
![Page 6: Section 13.6a The Unit Circle. The Unit Circle (like any circle) contains 360 ° It’s called the Unit Circle because the length of the radius is 1 π/2.](https://reader035.fdocuments.us/reader035/viewer/2022062718/56649ea85503460f94babe16/html5/thumbnails/6.jpg)
Values of the Unit Circle
60o
r = 1sin 60o =
cos 60o =
2
3,
2
1
3
2
1
2
![Page 7: Section 13.6a The Unit Circle. The Unit Circle (like any circle) contains 360 ° It’s called the Unit Circle because the length of the radius is 1 π/2.](https://reader035.fdocuments.us/reader035/viewer/2022062718/56649ea85503460f94babe16/html5/thumbnails/7.jpg)
Values of the Unit Circle
r = 1
45o
sin 135o =
2
2
2
2cos 135o =
2
2,
2
2
![Page 8: Section 13.6a The Unit Circle. The Unit Circle (like any circle) contains 360 ° It’s called the Unit Circle because the length of the radius is 1 π/2.](https://reader035.fdocuments.us/reader035/viewer/2022062718/56649ea85503460f94babe16/html5/thumbnails/8.jpg)
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Signs of Trigonometric Functions
Quadrant
I - All
AS
T C
All Students Take CalculusAll Students Take Calculus
++
+
Sin = Opp/HypCos = Adj/HypTan = Opp/Adj
-+
--
+++
II - Sin
III - TanIV - Cos
![Page 9: Section 13.6a The Unit Circle. The Unit Circle (like any circle) contains 360 ° It’s called the Unit Circle because the length of the radius is 1 π/2.](https://reader035.fdocuments.us/reader035/viewer/2022062718/56649ea85503460f94babe16/html5/thumbnails/9.jpg)
1.) using the unit circle convert each measure from degrees to radians
a) 150° b) 225° c) 480°
2.) using the unit circle convert each measure from radians to degrees
a) b) c)6
56
7 9
![Page 10: Section 13.6a The Unit Circle. The Unit Circle (like any circle) contains 360 ° It’s called the Unit Circle because the length of the radius is 1 π/2.](https://reader035.fdocuments.us/reader035/viewer/2022062718/56649ea85503460f94babe16/html5/thumbnails/10.jpg)
3.) use the unit circle to find the exact value of each
a) sin 120° b) tan 225°
4.) use the unit circle to find sine, cosine and tangent of each
a) b) 6
54
3
![Page 11: Section 13.6a The Unit Circle. The Unit Circle (like any circle) contains 360 ° It’s called the Unit Circle because the length of the radius is 1 π/2.](https://reader035.fdocuments.us/reader035/viewer/2022062718/56649ea85503460f94babe16/html5/thumbnails/11.jpg)
![Page 12: Section 13.6a The Unit Circle. The Unit Circle (like any circle) contains 360 ° It’s called the Unit Circle because the length of the radius is 1 π/2.](https://reader035.fdocuments.us/reader035/viewer/2022062718/56649ea85503460f94babe16/html5/thumbnails/12.jpg)
Homework
Worksheet 13-3B