Chapter 6 Trigonometric Ratios

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PROJECT TITLE
Trigonometric Ratios
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Target Audience
F.2 Students
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How Slides are going to be used ?
The Slide are going to be used during lesson
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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

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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)

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Adjacent , Opposite Side and Hypotenuse of a
Right Angle Triangle.
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Opposite side
hypotenuse
Adjacent side
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hypotenuse
Adjacent side
Opposite side
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Three Types Trigonometric Ratios

• There are 3 kinds of trigonometric ratios we will
  learn.
• sine ratio
• cosine ratio
• tangent ratio

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Sine Ratios

• Definition of Sine Ratio.
• Application of Sine Ratio.

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• Definition of Sine Ratio.

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If the hypotenuse equals to 1
Sin?
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• 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
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? 34.85? (corr to 2 d.p.)
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Exercise 2
In the figure, find y
y
Opposite Side
Sin35?
hypotenuses
35
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y
Sin35?
11
y 11 sin35?
y 6.31 (corr to 2.d.p.)
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Cosine Ratios

• Definition of Cosine.
• Relation of Cosine to the sides of right angle
  triangle.

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• Definition of Cosine Ratio.

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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
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In the figure, find cos ?
?
adjacent Side
cos?
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hypotenuses
3

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? 67.98? (corr to 2 d.p.)
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Exercise 4
In the figure, find x
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Adjacent Side
Cos 42?
42
hypotenuses
x
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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.

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• Definition of Tangent Ratio.

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