Transcript Chapter 6 Trigonometric Ratios

GROUP 5
Student
1 Chau Ping
Student ID
S98038000
2 Szeto Kwok Fai
S98037010
3 Moy Yee Ping
S98037350
Trigonometric Ratios
Contents
 Introduction to Trigonometric Ratios
 Unit Circle
 Adjacent , opposite side and hypotenuse of a
right angle triangle.
 Three types trigonometric ratios
 Conclusion
Introduction Trigonometric Ratios
Trigonometry (三角幾何) means “Triangle” and
“Measurement”
In F.2 we concentrated on right angle triangles.
Unit Circle
A Unit Circle Is a Circle With Radius Equals to 1
Unit.(We Always Choose Origin As Its centre)
Y
1 units
x
Hypotenuse of a Right Angle Triangle.
Opposite side


Opposite side
Three Types Trigonometric Ratios
There are 3 kinds of trigonometric
ratios we will learn.
sine ratio
cosine ratio
tangent ratio
Sine Ratios
 Definition of Sine Ratio.
 Application of Sine Ratio.
Definition of Sine Ratio.
1

If the hypotenuse equals to 1
Sin = Opposite sides
Definition of Sine Ratio.

For any right-angled triangle
Sin =
Opposite side
hypotenuses
Exercise 1
In the figure, find sin 
Sin =
=
=
Opposite Side
hypotenuses
4
7
34.85 (corr to 2 d.p.)

4
7
Exercise 2
In the figure, find y
Sin35 =
Sin35 =
y
Opposite Side
hypotenuses
y
11
y=
11 sin35
y=
6.31 (corr to 2.d.p.)
35°
11
Cosine Ratios
 Definition of Cosine.
 Relation of Cosine to the sides of right
angle triangle.
Definition of Cosine Ratio.
1

If the hypotenuse equals to 1
Cos =
Definition of Cosine Ratio.

For any right-angled triangle
Cos =
hypotenuses
Exercise 3
In the figure, find cos 
cos =
=
=
hypotenuses
3
8
67.98 (corr to 2 d.p.)
3

8
Exercise 4
In the figure, find x
Cos 42 =
Cos 42 =
x=
x=
6
42°
hypotenuses
6
x
6
Cos 42
8.07 (corr to 2.d.p.)
x
Tangent Ratios
 Definition of Tangent.
 Relation of Tangent to the sides of right
angle triangle.
Definition of Tangent Ratio.

For any right-angled triangle
tan =
Opposite Side
Exercise 5
3
In the figure, find tan 
tan =
=
=
Opposite side
3
5
78.69 (corr to 2 d.p.)
5

Exercise 6
In the figure, find z
tan 22 =
tan 22 =
z=
z=
z
Opposite side
5
z
5
tan 22
12.38 (corr to 2 d.p.)
5
22
Conclusion
opposite side
sin  
hypotenuse