Math L2 Module 11

Mathematics NQF Level 2 Downloaded from hlayiso.com *see terms and conditions Mathematics NQF Level 2

Solving problems by constructing and interpreting trigonometric models Module 11 Downloaded from hlayiso.com Mathematics NQF Level 2

The trigonometric functions sin θ, cos θ and tan θ Definitions of sine, cosine and tangent opposite  O  sin θ    hypotenuse  H  adjacent  A  cos θ    hypotenuse  H  opposite O tan θ    adjacent A Figure 11.3: Sides of a triangle Downloaded from hlayiso.com Unit 11.1

Consider two identical triangles: Figure 11.4: Sides of a triangle in relation to the reference angle Downloaded from hlayiso.com Unit 11.1

Learning activity 11.2 Downloaded from hlayiso.com Mathematics NQF Level 2

Given ΔABC, calculate: 1. the length of AC AC 2  AB2  BC 2 [Theorem of Pythagoras]  52  122  25  144  169  AC  13 Downloaded from hlayiso.com Learning activity 11.2

Given ΔABC, calculate: 2. sin A 12 sin A  13 Downloaded from hlayiso.com Learning activity 11.2

Given ΔABC, calculate: 3. cos A 5 cos A  13 Downloaded from hlayiso.com Learning activity 11.2

Given ΔABC, calculate: 4. tan A 12 tan A  5 Downloaded from hlayiso.com Learning activity 11.2

Given ΔABC, calculate: 5. sin C 5 sin C  13 Downloaded from hlayiso.com Learning activity 11.2

Given ΔABC, calculate: 6. cos C 12 cos C = 13 Downloaded from hlayiso.com Learning activity 11.2

Given ΔABC, calculate: 7. tan C 5 tan C = 12 Downloaded from hlayiso.com Learning activity 11.2

Learning activity 11.3 Downloaded from hlayiso.com Mathematics NQF Level 2

Calculate the other two ratios if: O 4 tan   A 3. tan   , 180° ≤ θ ≤ 270° 8 OP 2  AP 2  AO 2  82  4 2  OP  8,944 A 8 cos     0,894 H 8,944 O 4 sin     0, 447 H 8,944 LG Figure 11.3 Downloaded from hlayiso.com Learning activity 11.3

Learning activity 11.4 Downloaded from hlayiso.com Mathematics NQF Level 2

2. Given: 2.2 Calculate cos A A cos A  H 357,8  400  0, 895 Downloaded from hlayiso.com Learning activity 11.4

2. Given: 2.3 Calculate sin C O sin C  H 178,9  200  0, 895 Downloaded from hlayiso.com Learning activity 11.4

2. Given: ˆ 2.5 Calculate cos ADB ˆ A cos ADB  H 178,9  400  0, 447 Downloaded from hlayiso.com Learning activity 11.4

2. Given: ˆ 2.6 Calculate tan BDC ˆ O tan BDC  A 89, 4  178,9  0, 5 Downloaded from hlayiso.com Learning activity 11.4

2. Given: ˆ 2.10 Calculate cos BDC ˆ A cos BDC  H 178,9  200  0, 895 Downloaded from hlayiso.com Learning activity 11.4

2. Given: 2.11 Calculate  O 178,9 tan A = = A 357,8 tan A  0,5 tan 1 . tan A  tan 1 (0, 5) [Take tan 1 on both sides]   = tan 1 0,5  0 . 5 tan 1 on calculator     26,57 [If your calculator is set on "deg"] Downloaded from hlayiso.com Learning activity 11.4

2. Given: ˆ 2.12 Calculate ADB ˆ B ˆ A ADB ˆ  180 ˆ  180  90  26,57  ADB  63, 43 Downloaded from hlayiso.com Learning activity 11.4

Summative assessment Module 11 Downloaded from hlayiso.com Mathematics NQF Level 2

Click above to play this video. Downloaded from hlayiso.com Summative assessment – Module 11

3 2. Calculate the other two ratios if tan  4 3 y CAST Quadrant II: tan   = rule 4 x OP  x 2  y 2   4 2  32  OP  5 y x sin   cos   r r LG Figure 11.8: Diagram 1 3 4 sin   cos   5 Downloaded from hlayiso.com 5 Summative assessment – Module 11

3 2. Calculate the other two ratios if tan  4 (continued) 3 y Quadrant IV: tan   4 x y x sin   cos   r r 3 4 sin   cos  5 5 LG Figure 11.8: Diagram 2 Downloaded from hlayiso.com Summative assessment – Module 11

Downloaded from hlayiso.com Mathematics NQF Level 2