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 \(\triangle KLM\) met \(KM=47\text{,}\) \(\angle K=34\degree\) en \(\angle L=90\degree\text{.}\) |
a Cosinus in \(\triangle KLM\) geeft \(\cos(\angle K)={KL \over KM}\) ofwel \(\cos(34\degree)={KL \over 47}\text{.}\) 1p Hieruit volgt \(KL=47⋅\cos(34\degree)\text{.}\) 1p Dus \(KL≈39{,}0\text{.}\) 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 \(\triangle PQR\) met \(PQ=34\text{,}\) \(\angle P=40\degree\) en \(\angle Q=90\degree\text{.}\) |
a Cosinus in \(\triangle PQR\) geeft \(\cos(\angle P)={PQ \over PR}\) ofwel \(\cos(40\degree)={34 \over PR}\text{.}\) 1p Hieruit volgt \(PR={34 \over \cos(40\degree)}\text{.}\) 1p Dus \(PR≈44{,}4\text{.}\) 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 \(PQ=55\text{,}\) \(PR=76\) en \(\angle Q=90\degree\text{.}\) |
a Cosinus in \(\triangle PQR\) geeft \(\cos(\angle P)={PQ \over PR}\) ofwel \(\cos(\angle P)={55 \over 76}\text{.}\) 1p Hieruit volgt \(\angle P=\cos^{-1}({55 \over 76})\text{.}\) 1p Dus \(\angle P≈43{,}6\degree\text{.}\) 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 \(\triangle PQR\) met \(QR=65\text{,}\) \(\angle R=55\degree\) en \(\angle P=90\degree\text{.}\) |
a Sinus in \(\triangle PQR\) geeft \(\sin(\angle R)={PQ \over QR}\) ofwel \(\sin(55\degree)={PQ \over 65}\text{.}\) 1p Hieruit volgt \(PQ=65⋅\sin(55\degree)\text{.}\) 1p Dus \(PQ≈53{,}2\text{.}\) 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 \(\triangle PQR\) met \(QR=28\text{,}\) \(\angle P=33\degree\) en \(\angle Q=90\degree\text{.}\) |
a Sinus in \(\triangle PQR\) geeft \(\sin(\angle P)={QR \over PR}\) ofwel \(\sin(33\degree)={28 \over PR}\text{.}\) 1p Hieruit volgt \(PR={28 \over \sin(33\degree)}\text{.}\) 1p Dus \(PR≈51{,}4\text{.}\) 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 \(AC=38\text{,}\) \(AB=47\) en \(\angle C=90\degree\text{.}\) |
a Sinus in \(\triangle ABC\) geeft \(\sin(\angle B)={AC \over AB}\) ofwel \(\sin(\angle B)={38 \over 47}\text{.}\) 1p Hieruit volgt \(\angle B=\sin^{-1}({38 \over 47})\text{.}\) 1p Dus \(\angle B≈54{,}0\degree\text{.}\) 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 \(AC=50\text{,}\) \(\angle C=38\degree\) en \(\angle A=90\degree\text{.}\) |
a Tangens in \(\triangle ABC\) geeft \(\tan(\angle C)={AB \over AC}\) ofwel \(\tan(38\degree)={AB \over 50}\text{.}\) 1p Hieruit volgt \(AB=50⋅\tan(38\degree)\text{.}\) 1p Dus \(AB≈39{,}1\text{.}\) 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 \(BC=20\text{,}\) \(\angle A=37\degree\) en \(\angle B=90\degree\text{.}\) |
a Tangens in \(\triangle ABC\) geeft \(\tan(\angle A)={BC \over AB}\) ofwel \(\tan(37\degree)={20 \over AB}\text{.}\) 1p Hieruit volgt \(AB={20 \over \tan(37\degree)}\text{.}\) 1p Dus \(AB≈26{,}5\text{.}\) 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 \(\triangle KLM\) met \(KL=52\text{,}\) \(LM=48\) en \(\angle L=90\degree\text{.}\) |
a Tangens in \(\triangle KLM\) geeft \(\tan(\angle K)={LM \over KL}\) ofwel \(\tan(\angle K)={48 \over 52}\text{.}\) 1p Hieruit volgt \(\angle K=\tan^{-1}({48 \over 52})\text{.}\) 1p Dus \(\angle K≈42{,}7\degree\text{.}\) 1p |