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 \(PQ=48\text{,}\) \(\angle Q=58\degree\) en \(\angle R=90\degree\text{.}\) |
a Cosinus in \(\triangle PQR\) geeft \(\cos(\angle Q)={QR \over PQ}\) ofwel \(\cos(58\degree)={QR \over 48}\text{.}\) 1p Hieruit volgt \(QR=48⋅\cos(58\degree)\text{.}\) 1p Dus \(QR≈25{,}4\text{.}\) 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 \(QR=58\text{,}\) \(\angle Q=41\degree\) en \(\angle R=90\degree\text{.}\) |
a Cosinus in \(\triangle PQR\) geeft \(\cos(\angle Q)={QR \over PQ}\) ofwel \(\cos(41\degree)={58 \over PQ}\text{.}\) 1p Hieruit volgt \(PQ={58 \over \cos(41\degree)}\text{.}\) 1p Dus \(PQ≈76{,}9\text{.}\) 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 \(\triangle KLM\) met \(KL=50\text{,}\) \(KM=77\) en \(\angle L=90\degree\text{.}\) |
a Cosinus in \(\triangle KLM\) geeft \(\cos(\angle K)={KL \over KM}\) ofwel \(\cos(\angle K)={50 \over 77}\text{.}\) 1p Hieruit volgt \(\angle K=\cos^{-1}({50 \over 77})\text{.}\) 1p Dus \(\angle K≈49{,}5\degree\text{.}\) 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 \(PR=65\text{,}\) \(\angle P=33\degree\) en \(\angle Q=90\degree\text{.}\) |
a Sinus in \(\triangle PQR\) geeft \(\sin(\angle P)={QR \over PR}\) ofwel \(\sin(33\degree)={QR \over 65}\text{.}\) 1p Hieruit volgt \(QR=65⋅\sin(33\degree)\text{.}\) 1p Dus \(QR≈35{,}4\text{.}\) 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 \(QR=38\text{,}\) \(\angle P=34\degree\) en \(\angle Q=90\degree\text{.}\) |
a Sinus in \(\triangle PQR\) geeft \(\sin(\angle P)={QR \over PR}\) ofwel \(\sin(34\degree)={38 \over PR}\text{.}\) 1p Hieruit volgt \(PR={38 \over \sin(34\degree)}\text{.}\) 1p Dus \(PR≈68{,}0\text{.}\) 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 \(AB=36\text{,}\) \(BC=48\) en \(\angle A=90\degree\text{.}\) |
a Sinus in \(\triangle ABC\) geeft \(\sin(\angle C)={AB \over BC}\) ofwel \(\sin(\angle C)={36 \over 48}\text{.}\) 1p Hieruit volgt \(\angle C=\sin^{-1}({36 \over 48})\text{.}\) 1p Dus \(\angle C≈48{,}6\degree\text{.}\) 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 \(\triangle KLM\) met \(KL=28\text{,}\) \(\angle K=36\degree\) en \(\angle L=90\degree\text{.}\) |
a Tangens in \(\triangle KLM\) geeft \(\tan(\angle K)={LM \over KL}\) ofwel \(\tan(36\degree)={LM \over 28}\text{.}\) 1p Hieruit volgt \(LM=28⋅\tan(36\degree)\text{.}\) 1p Dus \(LM≈20{,}3\text{.}\) 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 \(AB=52\text{,}\) \(\angle C=41\degree\) en \(\angle A=90\degree\text{.}\) |
a Tangens in \(\triangle ABC\) geeft \(\tan(\angle C)={AB \over AC}\) ofwel \(\tan(41\degree)={52 \over AC}\text{.}\) 1p Hieruit volgt \(AC={52 \over \tan(41\degree)}\text{.}\) 1p Dus \(AC≈59{,}8\text{.}\) 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 \(LM=56\text{,}\) \(KM=40\) en \(\angle M=90\degree\text{.}\) |
a Tangens in \(\triangle KLM\) geeft \(\tan(\angle L)={KM \over LM}\) ofwel \(\tan(\angle L)={40 \over 56}\text{.}\) 1p Hieruit volgt \(\angle L=\tan^{-1}({40 \over 56})\text{.}\) 1p Dus \(\angle L≈35{,}5\degree\text{.}\) 1p |