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GRAAD 10
NOG OEFENINGE
Berekening van die trigonometriese funksies m.b.v 'n sakrekenaar : antwoorde.
MATHEMATICS
GRADE 10
MORE EXERCISES
Calculating the value of the trigonometrc functions using a pocket calculator : answers.
Antwoord / Answer 1.
1.1
sin 48,2° = 0,75
1.2
cos 34,7° = 0,82
1.3
tan 40,2° = 0,85
1
1
1
1.4
cosec 80° = —————
1.5
sec 62,6° = —————
1.6
cot 53,9° = —————
sin 80°
cos 62,6°
tan 53,9°
= 1,02
= 2,17
= 0,73
1.7
5 sin 18,3° = 5 x 0,31399...
1.8
8 cos 33,1° = 8 x 0,837718...
1.9
10 tan 42,7° = 10 x 0,92277..
= 1,57
= 6,70
= 9,23
7
3
8
1.10
7 cosec 18,6° = ————
1.11
3 sec 78,2° = —————
1.12
8 cot 62,3° = —————
sin 18,6°
cos 78,2°
tan 62,3°
= 21,95
= 14,67
= 4,20
1.13
tan 31,4° + cos 88,2° = 0,6104... + 0,91212....
1.14
sin 71,6° + cos 24,2° = 0,94888... + 0,91068....
= 1,52
= 1,86
1.15
tan 71,2° + sin 58,7° = 2,937481... + 0,854459...
1.16
sin 63,8° − cos 78,7° = 0,897258... + 0,195946....
= 3,79
= 0,70
Antwoord / Answer 2.
2.1
sin (A + B) = sin (41,3° + 28,6°)
2.2
sin A + sin B = sin 41,3° + sin 28,6°
= sin 69,9°
= 0,6600... + 0,4786...
= 0,94
= 1,14
2.3
cos (A − B) = cos (41,3° − 28,6°)
2.4
cos A − cos B = cos 41,3° − cos 28,6°
= cos 12,7°
= 0,7512... + 0,8779...
= 0,98
= − 0,13
2.5
tan 2B = tan (2 x 28,6°)
2.6
sin (2A − B) = sin (2 x 41,3° − 28,6°)
= tan 57,2°
= sin 54,0°
= 1,55
= 0,81
2.7
cos (3A − 2B) = cos (3 x 41,3° − 2 x 28,6°)
2.8
cos A X sin B = cos 41,3° X sin 28,6°
= cos 66,7°
= 0,7512... X 0,4786...
= 0,40
= 0,36
2.9
3 tan 2A − 5 cos B =
3 tan 2 x 41,3° − 5 cos 28,6°
= 3 tan 82,6° − 5 cos 28,6
= 3 x 7,6995... − 5 x 0,8779...
= 23,0987... − 4,3899...
= 18,71
Antwoord / Answer 3.
3.1
sin θ = 0,34
3.2
cos α = 0,851
3.3
tan Φ = 0,651
θ = 19,88°
α = 31,79°
Φ = 33,06°
3.4
sin α = 0,94
3.5
cos θ = 0,977
3.6
tan α = 0,408
α = 70,05°
θ = 12,31°
α = 22,20°
3.7
2 sin α = 0,622
3.8
4 cos θ = 3
3.9
2 tan θ = 3,662
sin α = 0,311
cos θ = 0,75
tan θ = 1,831
α = 18,12°
θ = 41,41°
θ = 61,36°
3.10
tan 2θ = 1,209
3.11
sin 3Φ = 0,99
3.12
sin 2α = 0,67
2θ = 50,4048...°
3Φ = 81,8903...°
2α = 42,0670...°
θ = 25,20°
Φ = 27,30°
α = 21,03°
3.13
cos (θ + 10°) = 0,66
3.14
sin (Φ + 18°) = 0,63
3.15
tan (θ + 21,3°) = 1,30
θ + 10° = 48,7001..°
Φ + 18° = 39,0501..°
θ + 21,3° = 52,4314..°
θ = 38,70°
Φ = 21,05°
θ = 31,13°
3.16
sin (α + 18,7°) = 0,94
3.17
cos (α − 18°) = 0,832
3.18
sin (θ − 21,2°) = 0,21
α + 18,7° = 70,0515...°
α − 18° = 33,6952...°
θ − 21,2° = 12,1223...°
α = 51,35°
α = 51,70°
θ = 33,32°
3.19
4 tan (48,3° − Φ) = 2,812
3.20
2 sin (θ + 17,3°) = 1,306
3.21
3 cos (α + 18,62°) = 0,989
tan (48,3° − Φ) = 0,703
sin (θ + 17,3°) = 0,653
cos (α + 18,62°) = 0,32966...
48,3° − Φ = 35,1072...°
θ + 17,3° = 40,7681...°
α + 18,62° = 70,7514...°
Φ = 13,19°
θ = 23,47°
α = 52,13°
3.22
5 tan (78,6° − Φ) = 5
3.23
2 sin (α + 12,4°) − 1 = 0
3.24
4 cos (88,3° − θ) − 2 = 0
tan (78,6° − Φ) = 1
sin (α + 12,4°) = 0,5
cos (88,3° − θ) = 0,5
78,6° − Φ = 45°
α + 12,4° = 30°
88,3° − θ = 60°
Φ = 33,60°
α = 17,60°
θ = 28,30°
3.25
5 − tan (68,2° + α) = 1
3.26
1,74 − 2 sin (θ + 28,4°) = 0
3.27
2 cos (α + 12°) − 1,74 = 0
tan (68,2° + α) = 4
2 sin (θ + 28,4°) = 1,74
2 cos (α + 12°) = 1,74
68,2° + α = 75,9637...°
sin (θ + 28,4°) = 0.87
cos (α + 12°) = 0,87
α = 75,9637...° − 68,2°
θ + 28,4° = 60,458639...°
α + 12° = 29,54136...°
α = 7,76°
θ = 32,06°
α = 17,54°