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Chapter 6 Trigonometric Ratios

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Trigonometric Ratios Contents Introduction to Trigonometric Ratios Unit Circle Adjacent , opposite side and hypotenuse of a right angle triangle. – PowerPoint PPT presentation

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Title: Chapter 6 Trigonometric Ratios


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(No Transcript)
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PROJECT TITLE
Trigonometric Ratios
3
Target Audience
F.2 Students
4
How Slides are going to be used ?
The Slide are going to be used during lesson
5
System Requirement
A computer with the following software
installed Power Point 97/2000
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Trigonometric Ratios
  • Contents
  • Introduction to Trigonometric Ratios
  • Unit Circle
  • Adjacent , opposite side and hypotenuse of a
    right angle triangle.
  • Three types trigonometric ratios
  • Conclusion

7
Introduction Trigonometric Ratios
Trigonometry (????) means Triangle and
Measurement
In F.2 we concentrated on right angle triangles.
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Unit Circle
  • A Unit Circle Is a Circle With Radius Equals to 1
    Unit.(We Always Choose Origin As Its centre)

9
Adjacent , Opposite Side and Hypotenuse of a
Right Angle Triangle.
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Opposite side
hypotenuse
Adjacent side
11
hypotenuse
Adjacent side
Opposite side
12
Three Types Trigonometric Ratios
  • There are 3 kinds of trigonometric ratios we will
    learn.
  • sine ratio
  • cosine ratio
  • tangent ratio

13
Sine Ratios
  • Definition of Sine Ratio.
  • Application of Sine Ratio.

14
  • Definition of Sine Ratio.

1
If the hypotenuse equals to 1
Sin?
15
  • Definition of Sine Ratio.

For any right-angled triangle
Sin?
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Exercise 1
In the figure, find sin ?
Opposite Side
Sin?
hypotenuses
4

7
? 34.85? (corr to 2 d.p.)
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Exercise 2
In the figure, find y
y
Opposite Side
Sin35?
hypotenuses
35
11
y
Sin35?
11
y 11 sin35?
y 6.31 (corr to 2.d.p.)
18
Cosine Ratios
  • Definition of Cosine.
  • Relation of Cosine to the sides of right angle
    triangle.

19
  • Definition of Cosine Ratio.

1
If the hypotenuse equals to 1
Cos?
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  • Definition of Cosine Ratio.

For any right-angled triangle
Cos?
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Exercise 3
3
In the figure, find cos ?
?
adjacent Side
cos?
8
hypotenuses
3

8
? 67.98? (corr to 2 d.p.)
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Exercise 4
In the figure, find x
6
Adjacent Side
Cos 42?
42
hypotenuses
x
6
Cos 42?
x
6
x
Cos 42?
x 8.07 (corr to 2.d.p.)
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Tangent Ratios
  • Definition of Tangent.
  • Relation of Tangent to the sides of right angle
    triangle.

24
  • Definition of Tangent Ratio.

For any right-angled triangle
tan?
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Exercise 5
3
In the figure, find tan ?
5
Opposite side
tan?
adjacent Side
?
3

5
? 78.69? (corr to 2 d.p.)
26
Exercise 6
In the figure, find z
z
22?
Opposite side
tan 22?
adjacent Side
5
5
tan 22?
z
5
z
tan 22?
z 12.38 (corr to 2 d.p.)
27
Conclusion
Make Sure that the triangle is right-angled
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END
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