Trigonometric Functions sine cosine and tangent Unit 4

Trigonometric Functions sine, cosine and tangent

Unit 4: Mathematics 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. 2

Re-Call

radians _Degrees S = r radians 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

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

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

Sine Wave

Cosine Wave

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

+ve −ve H O H A A O

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

y What are the coordinates of point ‘P’? P Sin 30º= 1 Cos 30º= 30° 180° 0°x Tan 30º= Q 2 Q 3 Q 1 Q 4 Sin All Q 2 180° 0° Q 3 Tan 2π π Q 1 Q 4 Cos 90° 180° 270° 360°

Draw the sin, cosine and tangent wave form for these values 1. 0 0. 8 0. 6 0. 4 0. 2 -0. 4 -0. 6 -0. 8 -1. 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360