Trigo Ratios

GROUP 5

Student 1 Chau Ping 2 Szeto Kwok Fai 3 Moy Yee Ping

Student ID S98038000 S98037010 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. 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

Adjacent , Opposite Side and Hypotenuse of a Right Angle Triangle.

se nu te

po hy

Opposite side

θ Adjacent side

φ

se nu te

po hy

Adjacent 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

θ If the hypotenuse equals to 1 Sinθ = Opposite sides

Definition of Sine Ratio.

θ For any right-angled triangle Sinθ =

Opposite side hypotenuses

Exercise 1

In the figure, find sin θ

Sinθ =

= θ=

Opposite Side hypotenuses 4 7 34.85° (corr to 2 d.p.)

θ 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

θ If the hypotenuse equals to 1 Cosθ =

Adjacent Side

Definition of Cosine Ratio.

θ For any right-angled triangle Cosθ =

Adjacent Side hypotenuses

Exercise 3

In the figure, find cos θ

cosθ =

= θ=

adjacent Side hypotenuses 3 8 67.98° (corr to 2 d.p.)

3

θ 8

Exercise 4 In the figure, find x

Cos 42° =

Cos 42° = x= x=

6

Adjacent Side

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.

θ For any right-angled triangle tanθ =

Opposite Side Adjacent Side

Exercise 5 3 In the figure, find tan θ

tanθ =

= θ=

Opposite side adjacent Side 3 5 78.69° (corr to 2 d.p.)

5

θ

Exercise 6 In the figure, find z

tan 22° =

tan 22° = z= z=

z

Opposite side adjacent Side 5 z 5 tan 22° 12.38 (corr to 2 d.p.)

5

22°

Conclusion opposite side sin θ = hypotenuse adjacent side cos θ = hypotenuse opposite side tan θ = adjacent side

Make Sure that the triangle is right-angled

END