Sinus, cosinus en tangens
14 - 9 oefeningen
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Cosinus (1)
007j - basis
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Getal & Ruimte (13e editie) - 3 havo - 6.4 Getal & Ruimte (13e editie) - 3 vwo - 6.4 |
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3p a Gegeven is \(\triangle PQR\) met \(PR=42\text{,}\) \(\angle P=44\degree\) en \(\angle Q=90\degree\text{.}\) |
a Cosinus in \(\triangle PQR\) geeft \(\cos(\angle P)={PQ \over PR}\) ofwel \(\cos(44\degree)={PQ \over 42}\text{.}\) 1p Hieruit volgt \(PQ=42⋅\cos(44\degree)\text{.}\) 1p Dus \(PQ≈30{,}2\text{.}\) 1p |
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Cosinus (2)
007k - basis
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Getal & Ruimte (13e editie) - 3 havo - 6.4 Getal & Ruimte (13e editie) - 3 vwo - 6.4 |
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3p a Gegeven is \(\triangle KLM\) met \(LM=60\text{,}\) \(\angle L=43\degree\) en \(\angle M=90\degree\text{.}\) |
a Cosinus in \(\triangle KLM\) geeft \(\cos(\angle L)={LM \over KL}\) ofwel \(\cos(43\degree)={60 \over KL}\text{.}\) 1p Hieruit volgt \(KL={60 \over \cos(43\degree)}\text{.}\) 1p Dus \(KL≈82{,}0\text{.}\) 1p |
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Cosinus (3)
007l - basis
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Getal & Ruimte (13e editie) - 3 havo - 6.4 Getal & Ruimte (13e editie) - 3 vwo - 6.4 |
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3p a Gegeven is \(\triangle PQR\) met \(PQ=58\text{,}\) \(PR=71\) en \(\angle Q=90\degree\text{.}\) |
a Cosinus in \(\triangle PQR\) geeft \(\cos(\angle P)={PQ \over PR}\) ofwel \(\cos(\angle P)={58 \over 71}\text{.}\) 1p Hieruit volgt \(\angle P=\cos^{-1}({58 \over 71})\text{.}\) 1p Dus \(\angle P≈35{,}2\degree\text{.}\) 1p |
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Sinus (1)
007g - basis
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Getal & Ruimte (13e editie) - 3 havo - 6.4 Getal & Ruimte (13e editie) - 3 vwo - 6.4 |
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3p a Gegeven is \(\triangle ABC\) met \(BC=69\text{,}\) \(\angle C=53\degree\) en \(\angle A=90\degree\text{.}\) |
a Sinus in \(\triangle ABC\) geeft \(\sin(\angle C)={AB \over BC}\) ofwel \(\sin(53\degree)={AB \over 69}\text{.}\) 1p Hieruit volgt \(AB=69⋅\sin(53\degree)\text{.}\) 1p Dus \(AB≈55{,}1\text{.}\) 1p |
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Sinus (2)
007h - basis
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Getal & Ruimte (13e editie) - 3 havo - 6.4 Getal & Ruimte (13e editie) - 3 vwo - 6.4 |
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3p a Gegeven is \(\triangle ABC\) met \(AC=51\text{,}\) \(\angle B=54\degree\) en \(\angle C=90\degree\text{.}\) |
a Sinus in \(\triangle ABC\) geeft \(\sin(\angle B)={AC \over AB}\) ofwel \(\sin(54\degree)={51 \over AB}\text{.}\) 1p Hieruit volgt \(AB={51 \over \sin(54\degree)}\text{.}\) 1p Dus \(AB≈63{,}0\text{.}\) 1p |
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Sinus (3)
007i - basis
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Getal & Ruimte (13e editie) - 3 havo - 6.4 Getal & Ruimte (13e editie) - 3 vwo - 6.4 |
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3p a Gegeven is \(\triangle ABC\) met \(AC=41\text{,}\) \(AB=59\) en \(\angle C=90\degree\text{.}\) |
a Sinus in \(\triangle ABC\) geeft \(\sin(\angle B)={AC \over AB}\) ofwel \(\sin(\angle B)={41 \over 59}\text{.}\) 1p Hieruit volgt \(\angle B=\sin^{-1}({41 \over 59})\text{.}\) 1p Dus \(\angle B≈44{,}0\degree\text{.}\) 1p |
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Tangens (1)
007m - basis
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Getal & Ruimte (13e editie) - 3 havo - 6.3 Getal & Ruimte (13e editie) - 3 vwo - 6.3 |
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3p a Gegeven is \(\triangle ABC\) met \(AB=55\text{,}\) \(\angle A=37\degree\) en \(\angle B=90\degree\text{.}\) |
a Tangens in \(\triangle ABC\) geeft \(\tan(\angle A)={BC \over AB}\) ofwel \(\tan(37\degree)={BC \over 55}\text{.}\) 1p Hieruit volgt \(BC=55⋅\tan(37\degree)\text{.}\) 1p Dus \(BC≈41{,}4\text{.}\) 1p |
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Tangens (2)
007n - basis
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Getal & Ruimte (13e editie) - 3 havo - 6.3 Getal & Ruimte (13e editie) - 3 vwo - 6.3 |
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3p a Gegeven is \(\triangle ABC\) met \(AC=32\text{,}\) \(\angle B=59\degree\) en \(\angle C=90\degree\text{.}\) |
a Tangens in \(\triangle ABC\) geeft \(\tan(\angle B)={AC \over BC}\) ofwel \(\tan(59\degree)={32 \over BC}\text{.}\) 1p Hieruit volgt \(BC={32 \over \tan(59\degree)}\text{.}\) 1p Dus \(BC≈19{,}2\text{.}\) 1p |
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Tangens (3)
007o - basis
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Getal & Ruimte (13e editie) - 3 havo - 6.3 Getal & Ruimte (13e editie) - 3 vwo - 6.3 |
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3p a Gegeven is \(\triangle ABC\) met \(AB=60\text{,}\) \(BC=22\) en \(\angle B=90\degree\text{.}\) |
a Tangens in \(\triangle ABC\) geeft \(\tan(\angle A)={BC \over AB}\) ofwel \(\tan(\angle A)={22 \over 60}\text{.}\) 1p Hieruit volgt \(\angle A=\tan^{-1}({22 \over 60})\text{.}\) 1p Dus \(\angle A≈20{,}1\degree\text{.}\) 1p |