Aim: How do we review concepts of trigonometry?

Introduction Trigonometric Ratios Trigonometry means “Triangle” and “Measurement”

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

 Opposite side hypotenuse Adjacent side

Pythagorean Theorem

 hypotenuse Adjacent side Opposite side

Three Types Trigonometric Ratios There are 3 kinds of trigonometric ratios we will learn. sine ratio cosine ratio tangent ratio

Definition of Sine Ratio. Application of Sine Ratio. Sine Ratios Definition of Sine Ratio. Application of Sine Ratio.

Definition of Sine Ratio. Opposite sides  Sin =

Definition of Sine Ratio.  Opposite side hypotenuses For any right-angled triangle Sin =

 Exercise 1 In the figure, find sin  4 Opposite Side Sin = 7 hypotenuses 4 = 7  = 34.85 (corr to 2 d.p.)

35° 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.)

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

Definition of Cosine Ratio.  Adjacent Side Cos =

Definition of Cosine Ratio.  hypotenuses Adjacent Side For any right-angled triangle Cos =

 Exercise 3 3 In the figure, find cos  adjacent Side cos = 8 hypotenuses 3 = 8  = 67.98 (corr to 2 d.p.)

42° Exercise 4 In the figure, find x 6 Adjacent Side Cos 42 = hypotenuses x 6 Cos 42 = x 6 x = Cos 42 x = 8.07 (corr to 2.d.p.)

Tangent Ratios Definition of Tangent. Relation of Tangent to the sides of right angle triangle.

Definition of Tangent Ratio. Opposite Side  Adjacent Side For any right-angled triangle tan =

 Exercise 5 3 In the figure, find tan  Opposite side 5 tan = adjacent Side  3 = 5  = 30.96 (corr to 2 d.p.)

22 Exercise 6 In the figure, find z z Opposite side tan 22 = adjacent Side 5 5 tan 22 = z 5 z = tan 22 z = 12.38 (corr to 2 d.p.)

Make Sure that the triangle is right-angled Conclusion Make Sure that the triangle is right-angled

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