Trigonometric Functions sine, cosine and tangent.

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Presentation transcript:

Trigonometric Functions sine, cosine and tangent

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.

Re-Call

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

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

Trigonometric Functions Trigonometric Functions

x y All ratios positive Sine ratio positive Tangent ratio positive Cosine ratio positive Rheol CAST Rule

Sine Wave

Cosine Wave

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

+ve − ve H A O H O A

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

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=

Draw the sin, cosine and tangent wave form for these values