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Berekening van die waarde van die trigonometriese funksies - spesiale hoeke : antwoorde
MATHEMATICS
GRADE 10
MORE EXERCISES
Calculating the value of the trigonometrc functions - special angles : answers.
Antwoord / Answer 1.
1
1
1
1.1
sin 30° = ——
1.2
cos 60° = ——
1.3
tan 45° = ——
2
2
1
= 0,5
= 0,5
= 1
2
√2
1
1.4
cosec 60° = ——
1.5
sec 45° = —— = √2
1.6
cot 60° = ——
√3
1
√3
1
1
√3
1
1.7
sin 45° + cos 45° = —— + ——
1.8
cos 30° + cos 60° = —— + ——
√2
√2
2
2
2
√3 + 1
= ——
= ————
√2
2
1
= ——
√2
√3
√2
1
1
1.9
tan 60° + sec 45° = —— + ——
1.10
sin 30° + cos 0° = —— + ——
1
1
2
1
3
= √3 + √2
= ——
2
1
1
√3
1
1.11
tan 45° − sin 90° = —— − ——
1.12
sin 60° + cos 60° = —— + ——
1
1
2
2
√3 + 1
= 1 − 1 = 0
= ————
2
1
1
√3
√2
1.13
cos 0° + cot 45° = —— + —— = 2
1.14
tan 60° − sec 45° = —— − ——
= √3 −√2
1
1
1
1
1
1
2
√3
1.15
cos 0° + cos 60° = —— + ——
1.16
cosec 60° x tan 60° = —— x ——
1
2
√3
1
= 1½ = 1,5
= 2
√3
√3
1
1
1.17
sin 60° x cos 30° = —— x ——
1.18
cos 45° + sin 30° = —— + ——
2
2
√2
2
3
2 + √2
= ——
= ————
4
2√2
√3
√3
2
1
1.19
cos 30° × tan 60° = —— × ——
1.20
cosec 60° × tan 30° = —— × ——
2
1
√3
√3
3
2
= ——
= ——
2
3
1
1
√3
1
1.21
cos 45° . sin 45° + sin 60° . tan 30°
= —— × —— + —— × ——
√2
√2
2
√3
1
1
= —— + ——
2
2
= 1
Antwoord / Answer 2.
2.1
cos α = 0,5
2.2
tan θ = √3
2.3
sin Φ = 0,5
α = 60°
θ = 60°
Φ = 30°
2
1
2.4
tan θ = 1
2.5
cosec α = ——
2.6
tan θ = ——
√3
√3
α = 45°
α = 60°
Φ = 30°
1
1
√3
2.7
cos θ = ——
2.8
sin α = ——
2.9
sin Φ = ——
2
√2
2
α = 60°
α = 45°
Φ = 60°
1
2
√2
2.10
cot θ = ——
2.11
cosec α = ——
2.12
sec Φ = ——
√3
√3
1
θ = 60°
α = 60°
Φ = 45°
1
√3
1
2.13
sin (α + 14°) = ——
2.14
cos (θ − 22°) = ——
2.15
tan (Φ − 40°) = ——
2
2
√3
α + 14° = 30°
θ − 22° = 30°
Φ − 40° = 30°
α = 30° − 14°
θ = 30° + 22°
Φ = 30° + 40°
α = 16°
α = 52°
Φ = 70°