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 \(PQ=44\text{,}\) \(\angle Q=51\degree\) en \(\angle R=90\degree\text{.}\) |
a Cosinus in \(\triangle PQR\) geeft \(\cos(\angle Q)={QR \over PQ}\) ofwel \(\cos(51\degree)={QR \over 44}\text{.}\) 1p Hieruit volgt \(QR=44⋅\cos(51\degree)\text{.}\) 1p Dus \(QR≈27{,}7\text{.}\) 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 \(PR=36\text{,}\) \(\angle R=52\degree\) en \(\angle P=90\degree\text{.}\) |
a Cosinus in \(\triangle PQR\) geeft \(\cos(\angle R)={PR \over QR}\) ofwel \(\cos(52\degree)={36 \over QR}\text{.}\) 1p Hieruit volgt \(QR={36 \over \cos(52\degree)}\text{.}\) 1p Dus \(QR≈58{,}5\text{.}\) 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 \(LM=37\text{,}\) \(KL=52\) en \(\angle M=90\degree\text{.}\) |
a Cosinus in \(\triangle KLM\) geeft \(\cos(\angle L)={LM \over KL}\) ofwel \(\cos(\angle L)={37 \over 52}\text{.}\) 1p Hieruit volgt \(\angle L=\cos^{-1}({37 \over 52})\text{.}\) 1p Dus \(\angle L≈44{,}6\degree\text{.}\) 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 \(\triangle KLM\) met \(KL=72\text{,}\) \(\angle L=43\degree\) en \(\angle M=90\degree\text{.}\) |
a Sinus in \(\triangle KLM\) geeft \(\sin(\angle L)={KM \over KL}\) ofwel \(\sin(43\degree)={KM \over 72}\text{.}\) 1p Hieruit volgt \(KM=72⋅\sin(43\degree)\text{.}\) 1p Dus \(KM≈49{,}1\text{.}\) 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 \(AC=27\text{,}\) \(\angle B=37\degree\) en \(\angle C=90\degree\text{.}\) |
a Sinus in \(\triangle ABC\) geeft \(\sin(\angle B)={AC \over AB}\) ofwel \(\sin(37\degree)={27 \over AB}\text{.}\) 1p Hieruit volgt \(AB={27 \over \sin(37\degree)}\text{.}\) 1p Dus \(AB≈44{,}9\text{.}\) 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 \(\triangle PQR\) met \(QR=23\text{,}\) \(PR=30\) en \(\angle Q=90\degree\text{.}\) |
a Sinus in \(\triangle PQR\) geeft \(\sin(\angle P)={QR \over PR}\) ofwel \(\sin(\angle P)={23 \over 30}\text{.}\) 1p Hieruit volgt \(\angle P=\sin^{-1}({23 \over 30})\text{.}\) 1p Dus \(\angle P≈50{,}1\degree\text{.}\) 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 \(BC=59\text{,}\) \(\angle B=51\degree\) en \(\angle C=90\degree\text{.}\) |
a Tangens in \(\triangle ABC\) geeft \(\tan(\angle B)={AC \over BC}\) ofwel \(\tan(51\degree)={AC \over 59}\text{.}\) 1p Hieruit volgt \(AC=59⋅\tan(51\degree)\text{.}\) 1p Dus \(AC≈72{,}9\text{.}\) 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 \(\triangle KLM\) met \(KL=27\text{,}\) \(\angle M=34\degree\) en \(\angle K=90\degree\text{.}\) |
a Tangens in \(\triangle KLM\) geeft \(\tan(\angle M)={KL \over KM}\) ofwel \(\tan(34\degree)={27 \over KM}\text{.}\) 1p Hieruit volgt \(KM={27 \over \tan(34\degree)}\text{.}\) 1p Dus \(KM≈40{,}0\text{.}\) 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 \(KL=21\text{,}\) \(LM=26\) en \(\angle L=90\degree\text{.}\) |
a Tangens in \(\triangle KLM\) geeft \(\tan(\angle K)={LM \over KL}\) ofwel \(\tan(\angle K)={26 \over 21}\text{.}\) 1p Hieruit volgt \(\angle K=\tan^{-1}({26 \over 21})\text{.}\) 1p Dus \(\angle K≈51{,}1\degree\text{.}\) 1p |