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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
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.
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
Adjacent , Opposite Side and Adjacent , Opposite Side and Hypotenuse of a Right Angle Hypotenuse of a Right Angle
TriangleTriangle..
Adjacent side
Opposite side
hypotenuse
hypotenuse
Adjacent side
Opposite side
There are 3 kinds of trigonometric ratios we will learn.
sine ratio
cosine ratio
tangent ratio
Three Types Trigonometric Three Types Trigonometric RatiosRatios
Sine RatiosSine 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
4
7
In the figure, find sin
Sin = Opposite Side
hypotenuses
= 47
= 34.85 (corr to 2 d.p.)
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
Cosine RatiosCosine 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 = Adjacent Side
Definition of Cosine Ratio.
For any right-angled triangle
Cos = hypotenuses
Adjacent Side
Exercise 3
3
8
In the figure, find cos
cos = adjacent Side
hypotenuses
= 38
= 67.98 (corr to 2 d.p.)
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
Tangent RatiosTangent Ratios
Definition of Tangent. Relation of Tangent to the sides of
right angle triangle.
Definition of Tangent Ratio.
For any right-angled triangle
tan = Adjacent Side
Opposite Side
Exercise 5
3
5
In the figure, find tan
tan = adjacent Side
Opposite side
= 35
= 78.69 (corr to 2 d.p.)
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 =
ConclusionConclusion
hypotenuse
side oppositesin
hypotenuse
sidedjacent acos
sidedjacent a
side oppositetan
Make Sure that the
triangle is right-angled
END
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