Download - 4.4 Trigonometric Functions of Any Angle
![Page 1: 4.4 Trigonometric Functions of Any Angle](https://reader035.vdocuments.site/reader035/viewer/2022071712/56812a67550346895d8de74f/html5/thumbnails/1.jpg)
4.4 Trigonometric 4.4 Trigonometric Functions of Any Functions of Any
AngleAngle
![Page 2: 4.4 Trigonometric Functions of Any Angle](https://reader035.vdocuments.site/reader035/viewer/2022071712/56812a67550346895d8de74f/html5/thumbnails/2.jpg)
Let be an angle in Standard position and (x,y) on the terminal side
Let r ≠ 0
22 yxr
x
yTan
r
xCos
r
ySin
y
xCot
x
rSec
y
rCsc
![Page 3: 4.4 Trigonometric Functions of Any Angle](https://reader035.vdocuments.site/reader035/viewer/2022071712/56812a67550346895d8de74f/html5/thumbnails/3.jpg)
Let (-5,12) be a point on the terminal side of
Find the Sin, Cos and Tan
5
12
13
5
13
12
Tan
Cos
Sin
13169
125 22
r
r
Tan
Cos
Sin
Tan
Cos
Sin
Tan
Cos
Sin
Tan
Cos
Sin
![Page 4: 4.4 Trigonometric Functions of Any Angle](https://reader035.vdocuments.site/reader035/viewer/2022071712/56812a67550346895d8de74f/html5/thumbnails/4.jpg)
Reference Angles
What is the value of Sin 30º and Sin 150º ?
'
![Page 5: 4.4 Trigonometric Functions of Any Angle](https://reader035.vdocuments.site/reader035/viewer/2022071712/56812a67550346895d8de74f/html5/thumbnails/5.jpg)
Reference Angles
What is the value of Sin 30º and Sin 150º ?
Why not just use Sin 30º
Good news you can,
30º is the reference angle for 150º
But Cos 30º ≠ Cos 150º;
How are they related?
'
![Page 6: 4.4 Trigonometric Functions of Any Angle](https://reader035.vdocuments.site/reader035/viewer/2022071712/56812a67550346895d8de74f/html5/thumbnails/6.jpg)
Reference Angles
How to find a Reference Angle.
All reference angles are
During a Code Blue you need to get into the closest classroom; the reference angle is the closest angle to 180º or 360º.
'
2'0
![Page 7: 4.4 Trigonometric Functions of Any Angle](https://reader035.vdocuments.site/reader035/viewer/2022071712/56812a67550346895d8de74f/html5/thumbnails/7.jpg)
Reference Angles
Finding the reference angle
What is the reference angle of 110º ?
What is the reference angle of 284º ?
What about 72º ?
'
![Page 8: 4.4 Trigonometric Functions of Any Angle](https://reader035.vdocuments.site/reader035/viewer/2022071712/56812a67550346895d8de74f/html5/thumbnails/8.jpg)
Reference Angles
Finding the reference angle
What is the reference angle of ?
What is the reference angle of ?
What about 1.8 radians ?
'
4
5
3
5
![Page 9: 4.4 Trigonometric Functions of Any Angle](https://reader035.vdocuments.site/reader035/viewer/2022071712/56812a67550346895d8de74f/html5/thumbnails/9.jpg)
What is the exact value of Sin
What is the reference angle of
4
7
4
7
![Page 10: 4.4 Trigonometric Functions of Any Angle](https://reader035.vdocuments.site/reader035/viewer/2022071712/56812a67550346895d8de74f/html5/thumbnails/10.jpg)
What is the exact value of Sin
What is the reference angle of
What is
4
7
4
7
4
4
Sin
![Page 11: 4.4 Trigonometric Functions of Any Angle](https://reader035.vdocuments.site/reader035/viewer/2022071712/56812a67550346895d8de74f/html5/thumbnails/11.jpg)
What is the exact value of Sin
What is the reference angle of
What is
What Quadrant is in ?
4
7
4
7
4
2
2
4
Sin
4
7
![Page 12: 4.4 Trigonometric Functions of Any Angle](https://reader035.vdocuments.site/reader035/viewer/2022071712/56812a67550346895d8de74f/html5/thumbnails/12.jpg)
What is the exact value of Sin
What is the reference angle of
What is
What Quadrant is in ?
So
4
7
4
7
4
2
2
4
Sin
4
7
2
2
4
7
Sin
![Page 13: 4.4 Trigonometric Functions of Any Angle](https://reader035.vdocuments.site/reader035/viewer/2022071712/56812a67550346895d8de74f/html5/thumbnails/13.jpg)
Find Sec
What is the coterminal angle with ?
What quadrant is in?
4
11
4
11
4
4
32
4
11
4
11
![Page 14: 4.4 Trigonometric Functions of Any Angle](https://reader035.vdocuments.site/reader035/viewer/2022071712/56812a67550346895d8de74f/html5/thumbnails/14.jpg)
Find Sec
So the we need to find
4
11
22
22
2
2
2
2
1
4cos
1
24
11
Sec
![Page 15: 4.4 Trigonometric Functions of Any Angle](https://reader035.vdocuments.site/reader035/viewer/2022071712/56812a67550346895d8de74f/html5/thumbnails/15.jpg)
Using Trigonometric IdentitiesGiven: Find
22
3
3
2
and
Cos
Tan
and
Sin
9
5sin
1sin9
4
1sin3
2
2
2
22
3
5sin
9
5sin
![Page 16: 4.4 Trigonometric Functions of Any Angle](https://reader035.vdocuments.site/reader035/viewer/2022071712/56812a67550346895d8de74f/html5/thumbnails/16.jpg)
Using Trigonometric IdentitiesGiven: Find
22
3
3
2
and
Cos
Tan
and
Sin
9
5sin
1sin9
4
1sin3
2
2
2
22
3
5sin
9
5sin
2
5
3235
Tan
![Page 17: 4.4 Trigonometric Functions of Any Angle](https://reader035.vdocuments.site/reader035/viewer/2022071712/56812a67550346895d8de74f/html5/thumbnails/17.jpg)
HomeworkHomework
Page 297 – 299Page 297 – 299
##3, 9, 16, 22, 3, 9, 16, 22,
28, 34, 40 ,46, 28, 34, 40 ,46,
52, 58, 64, 74, 52, 58, 64, 74,
82, 90, 96 82, 90, 96
![Page 18: 4.4 Trigonometric Functions of Any Angle](https://reader035.vdocuments.site/reader035/viewer/2022071712/56812a67550346895d8de74f/html5/thumbnails/18.jpg)
HomeworkHomework
Page 297 – 299Page 297 – 299
## 6, 13, 19, 25, 6, 13, 19, 25,
31, 37, 43, 49, 31, 37, 43, 49,
55, 61, 70, 78, 55, 61, 70, 78,
86, 94, 9786, 94, 97