1. Trigonometric Functions sine, cosine and tangent

2. 2 Aims Initiate the learner into the trigonometric functions. Objectives Identify the variety of wave forms sine cosine and tangent. Sketch each of the three trigonometric functions over a complete cycle.

3. Re-Call

4. radians _ Degrees To convert from degrees to radians, multiply by ((PI)/180 o ). e.g. 60 degrees = 60 x π /180 = 1.047 radians To convert from radians to degrees, multiply by (180 o /(PI)). e.g. 2 radians = 2 x 180/π = 114.59 degrees  r S radians

5. Find the length of the arc and the area of the sector for the following circles: Convert the following into degrees:  S r

6. Trigonometric Functions Trigonometric Functions

7. -4 -3 -2 -1 0 1 2 3 4 4 3 2 1 -4 -3 -2 0 x y All ratios positive Sine ratio positive Tangent ratio positive Cosine ratio positive Rheol CAST Rule

8. Sine Wave

9. Cosine Wave

10. Tangent Wave Tangent is a ratio of sine/cosine Tan x = sin x cosx

11. +ve − ve H A O H O A

12. 30° 60° 120° 150° 210° 240° 300° 330° 90°180°270° 360° 1

13. P 180° 0° 30° 1 y x Q1Q2Q3Q4 2ππ 360°180° 90° 270° 180° 0° Q2 Q1 Q3Q4 All TanCos Sin What are the coordinates of point ‘P’? Sin 30º= Cos 30º= Tan 30º=

14. 20100806040140120240220200180260160280340300320360 0.2 0.4 0.6 0.8 1.0 -0.2 -0.4 -0.6 -0.8 Draw the sin, cosine and tangent wave form for these values