Trigonometric Ratios
Transcript of Trigonometric Ratios
![Page 1: Trigonometric Ratios](https://reader033.fdocument.pub/reader033/viewer/2022051208/546a8b44b4af9f59788b4839/html5/thumbnails/1.jpg)
GROUP 5
![Page 2: Trigonometric Ratios](https://reader033.fdocument.pub/reader033/viewer/2022051208/546a8b44b4af9f59788b4839/html5/thumbnails/2.jpg)
Student Student ID
1 Chau Ping S98038000
2 Szeto Kwok Fai S98037010
3 Moy Yee Ping S98037350
![Page 3: Trigonometric Ratios](https://reader033.fdocument.pub/reader033/viewer/2022051208/546a8b44b4af9f59788b4839/html5/thumbnails/3.jpg)
![Page 4: Trigonometric Ratios](https://reader033.fdocument.pub/reader033/viewer/2022051208/546a8b44b4af9f59788b4839/html5/thumbnails/4.jpg)
![Page 5: Trigonometric Ratios](https://reader033.fdocument.pub/reader033/viewer/2022051208/546a8b44b4af9f59788b4839/html5/thumbnails/5.jpg)
![Page 6: Trigonometric Ratios](https://reader033.fdocument.pub/reader033/viewer/2022051208/546a8b44b4af9f59788b4839/html5/thumbnails/6.jpg)
![Page 7: Trigonometric Ratios](https://reader033.fdocument.pub/reader033/viewer/2022051208/546a8b44b4af9f59788b4839/html5/thumbnails/7.jpg)
![Page 8: Trigonometric Ratios](https://reader033.fdocument.pub/reader033/viewer/2022051208/546a8b44b4af9f59788b4839/html5/thumbnails/8.jpg)
Trigonometric RatiosTrigonometric Ratios
Contents Introduction to Trigonometric Ratios
Unit Circle
Adjacent , opposite side and hypotenuse of a right angle triangle.
Three types trigonometric ratios
Conclusion
![Page 9: Trigonometric Ratios](https://reader033.fdocument.pub/reader033/viewer/2022051208/546a8b44b4af9f59788b4839/html5/thumbnails/9.jpg)
Trigonometry (Trigonometry ( 三角幾何三角幾何 )) means “Triangle” means “Triangle” and “Measurement”and “Measurement”
Introduction Trigonometric Introduction Trigonometric RatiosRatios
In F.2 we concentrated on right angle trianglesIn F.2 we concentrated on right angle triangles.
![Page 10: Trigonometric Ratios](https://reader033.fdocument.pub/reader033/viewer/2022051208/546a8b44b4af9f59788b4839/html5/thumbnails/10.jpg)
Unit CircleUnit Circle
A Unit Circle Is a Circle With Radius Equals to 1 Unit.(We Always Choose Origin As Its centre)
1 units
x
Y
![Page 11: Trigonometric Ratios](https://reader033.fdocument.pub/reader033/viewer/2022051208/546a8b44b4af9f59788b4839/html5/thumbnails/11.jpg)
Adjacent , Opposite Side and Adjacent , Opposite Side and Hypotenuse of a Right Angle Hypotenuse of a Right Angle
TriangleTriangle..
![Page 12: Trigonometric Ratios](https://reader033.fdocument.pub/reader033/viewer/2022051208/546a8b44b4af9f59788b4839/html5/thumbnails/12.jpg)
Adjacent side
Opposite side
hypotenuse
![Page 13: Trigonometric Ratios](https://reader033.fdocument.pub/reader033/viewer/2022051208/546a8b44b4af9f59788b4839/html5/thumbnails/13.jpg)
hypotenuse
Adjacent side
Opposite side
![Page 14: Trigonometric Ratios](https://reader033.fdocument.pub/reader033/viewer/2022051208/546a8b44b4af9f59788b4839/html5/thumbnails/14.jpg)
There are 3 kinds of trigonometric ratios we will learn.
sine ratio
cosine ratio
tangent ratio
Three Types Trigonometric Three Types Trigonometric RatiosRatios
![Page 15: Trigonometric Ratios](https://reader033.fdocument.pub/reader033/viewer/2022051208/546a8b44b4af9f59788b4839/html5/thumbnails/15.jpg)
Sine RatiosSine Ratios
Definition of Sine Ratio. Application of Sine Ratio.
![Page 16: Trigonometric Ratios](https://reader033.fdocument.pub/reader033/viewer/2022051208/546a8b44b4af9f59788b4839/html5/thumbnails/16.jpg)
Definition of Sine Ratio.
1
If the hypotenuse equals to 1
Sin = Opposite sides
![Page 17: Trigonometric Ratios](https://reader033.fdocument.pub/reader033/viewer/2022051208/546a8b44b4af9f59788b4839/html5/thumbnails/17.jpg)
Definition of Sine Ratio.
For any right-angled triangle
Sin = Opposite side
hypotenuses
![Page 18: Trigonometric Ratios](https://reader033.fdocument.pub/reader033/viewer/2022051208/546a8b44b4af9f59788b4839/html5/thumbnails/18.jpg)
Exercise 1
4
7
In the figure, find sin
Sin = Opposite Side
hypotenuses
= 47
= 34.85 (corr to 2 d.p.)
![Page 19: Trigonometric Ratios](https://reader033.fdocument.pub/reader033/viewer/2022051208/546a8b44b4af9f59788b4839/html5/thumbnails/19.jpg)
Exercise 2
11
In the figure, find y
Sin35 = Opposite Side
hypotenuses
y11
y = 6.31 (corr to 2.d.p.)
3535°°
y
Sin35 =
y = 11 sin35
![Page 20: Trigonometric Ratios](https://reader033.fdocument.pub/reader033/viewer/2022051208/546a8b44b4af9f59788b4839/html5/thumbnails/20.jpg)
Cosine RatiosCosine Ratios
Definition of Cosine. Relation of Cosine to the sides of right
angle triangle.
![Page 21: Trigonometric Ratios](https://reader033.fdocument.pub/reader033/viewer/2022051208/546a8b44b4af9f59788b4839/html5/thumbnails/21.jpg)
Definition of Cosine Ratio.
1
If the hypotenuse equals to 1
Cos = Adjacent Side
![Page 22: Trigonometric Ratios](https://reader033.fdocument.pub/reader033/viewer/2022051208/546a8b44b4af9f59788b4839/html5/thumbnails/22.jpg)
Definition of Cosine Ratio.
For any right-angled triangle
Cos = hypotenuses
Adjacent Side
![Page 23: Trigonometric Ratios](https://reader033.fdocument.pub/reader033/viewer/2022051208/546a8b44b4af9f59788b4839/html5/thumbnails/23.jpg)
Exercise 3
3
8
In the figure, find cos
cos = adjacent Side
hypotenuses
= 38
= 67.98 (corr to 2 d.p.)
![Page 24: Trigonometric Ratios](https://reader033.fdocument.pub/reader033/viewer/2022051208/546a8b44b4af9f59788b4839/html5/thumbnails/24.jpg)
Exercise 4
6
In the figure, find x
Cos 42 = Adjacent Side
hypotenuses
6x
x = 8.07 (corr to 2.d.p.)
4242°°
x
Cos 42 =
x =
6Cos 42
![Page 25: Trigonometric Ratios](https://reader033.fdocument.pub/reader033/viewer/2022051208/546a8b44b4af9f59788b4839/html5/thumbnails/25.jpg)
Tangent RatiosTangent Ratios
Definition of Tangent. Relation of Tangent to the sides of
right angle triangle.
![Page 26: Trigonometric Ratios](https://reader033.fdocument.pub/reader033/viewer/2022051208/546a8b44b4af9f59788b4839/html5/thumbnails/26.jpg)
Definition of Tangent Ratio.
For any right-angled triangle
tan = Adjacent Side
Opposite Side
![Page 27: Trigonometric Ratios](https://reader033.fdocument.pub/reader033/viewer/2022051208/546a8b44b4af9f59788b4839/html5/thumbnails/27.jpg)
Exercise 5
3
5
In the figure, find tan
tan = adjacent Side
Opposite side
= 35
= 78.69 (corr to 2 d.p.)
![Page 28: Trigonometric Ratios](https://reader033.fdocument.pub/reader033/viewer/2022051208/546a8b44b4af9f59788b4839/html5/thumbnails/28.jpg)
Exercise 6
z
5
In the figure, find z
tan 22 = adjacent Side
Opposite side
5
z
z = 12.38 (corr to 2 d.p.)
2222
tan 22 =
5
tan 22z =
![Page 29: Trigonometric Ratios](https://reader033.fdocument.pub/reader033/viewer/2022051208/546a8b44b4af9f59788b4839/html5/thumbnails/29.jpg)
ConclusionConclusion
hypotenuse
side oppositesin
hypotenuse
sidedjacent acos
sidedjacent a
side oppositetan
Make Sure that the
triangle is right-angled
![Page 30: Trigonometric Ratios](https://reader033.fdocument.pub/reader033/viewer/2022051208/546a8b44b4af9f59788b4839/html5/thumbnails/30.jpg)
END