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