Sinus, cosinus en tangens
14 - 9 oefeningen
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Cosinus (1)
007j - Sinus, cosinus en tangens - basis - 0ms
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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 Gegeven is \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) met \(A\kern{-.8pt}C=42\text{,}\) \(\angle A=49\degree\) en \(\angle B=90\degree\text{.}\) |
○ Cosinus in \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) geeft \(\cos(\angle A)={A\kern{-.8pt}B \over A\kern{-.8pt}C}\) ofwel \(\cos(49\degree)={A\kern{-.8pt}B \over 42}\text{.}\) 1p ○ Hieruit volgt \(A\kern{-.8pt}B=42⋅\cos(49\degree)\text{.}\) 1p ○ Dus \(A\kern{-.8pt}B≈27{,}6\text{.}\) 1p |
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Cosinus (2)
007k - Sinus, cosinus en tangens - basis - 0ms
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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 Gegeven is \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) met \(B\kern{-.8pt}C=59\text{,}\) \(\angle B=39\degree\) en \(\angle C=90\degree\text{.}\) |
○ Cosinus in \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) geeft \(\cos(\angle B)={B\kern{-.8pt}C \over A\kern{-.8pt}B}\) ofwel \(\cos(39\degree)={59 \over A\kern{-.8pt}B}\text{.}\) 1p ○ Hieruit volgt \(A\kern{-.8pt}B={59 \over \cos(39\degree)}\text{.}\) 1p ○ Dus \(A\kern{-.8pt}B≈75{,}9\text{.}\) 1p |
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Cosinus (3)
007l - Sinus, cosinus en tangens - basis - 1ms
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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 Gegeven is \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) met \(A\kern{-.8pt}C=24\text{,}\) \(B\kern{-.8pt}C=56\) en \(\angle A=90\degree\text{.}\) |
○ Cosinus in \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) geeft \(\cos(\angle C)={A\kern{-.8pt}C \over B\kern{-.8pt}C}\) ofwel \(\cos(\angle C)={24 \over 56}\text{.}\) 1p ○ Hieruit volgt \(\angle C=\cos^{-1}({24 \over 56})\text{.}\) 1p ○ Dus \(\angle C≈64{,}6\degree\text{.}\) 1p |
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Sinus (1)
007g - Sinus, cosinus en tangens - basis - 0ms
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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 Gegeven is \(\triangle K\kern{-.8pt}L\kern{-.8pt}M\) met \(K\kern{-.8pt}L=48\text{,}\) \(\angle L=54\degree\) en \(\angle M=90\degree\text{.}\) |
○ Sinus in \(\triangle K\kern{-.8pt}L\kern{-.8pt}M\) geeft \(\sin(\angle L)={K\kern{-.8pt}M \over K\kern{-.8pt}L}\) ofwel \(\sin(54\degree)={K\kern{-.8pt}M \over 48}\text{.}\) 1p ○ Hieruit volgt \(K\kern{-.8pt}M=48⋅\sin(54\degree)\text{.}\) 1p ○ Dus \(K\kern{-.8pt}M≈38{,}8\text{.}\) 1p |
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Sinus (2)
007h - Sinus, cosinus en tangens - basis - 0ms
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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 Gegeven is \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) met \(A\kern{-.8pt}B=41\text{,}\) \(\angle C=32\degree\) en \(\angle A=90\degree\text{.}\) |
○ Sinus in \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) geeft \(\sin(\angle C)={A\kern{-.8pt}B \over B\kern{-.8pt}C}\) ofwel \(\sin(32\degree)={41 \over B\kern{-.8pt}C}\text{.}\) 1p ○ Hieruit volgt \(B\kern{-.8pt}C={41 \over \sin(32\degree)}\text{.}\) 1p ○ Dus \(B\kern{-.8pt}C≈77{,}4\text{.}\) 1p |
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Sinus (3)
007i - Sinus, cosinus en tangens - basis - 0ms
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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 Gegeven is \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) met \(P\kern{-.8pt}Q=43\text{,}\) \(Q\kern{-.8pt}R=48\) en \(\angle P=90\degree\text{.}\) |
○ Sinus in \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) geeft \(\sin(\angle R)={P\kern{-.8pt}Q \over Q\kern{-.8pt}R}\) ofwel \(\sin(\angle R)={43 \over 48}\text{.}\) 1p ○ Hieruit volgt \(\angle R=\sin^{-1}({43 \over 48})\text{.}\) 1p ○ Dus \(\angle R≈63{,}6\degree\text{.}\) 1p |
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Tangens (1)
007m - Sinus, cosinus en tangens - basis - 0ms
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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 Gegeven is \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) met \(Q\kern{-.8pt}R=21\text{,}\) \(\angle Q=48\degree\) en \(\angle R=90\degree\text{.}\) |
○ Tangens in \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) geeft \(\tan(\angle Q)={P\kern{-.8pt}R \over Q\kern{-.8pt}R}\) ofwel \(\tan(48\degree)={P\kern{-.8pt}R \over 21}\text{.}\) 1p ○ Hieruit volgt \(P\kern{-.8pt}R=21⋅\tan(48\degree)\text{.}\) 1p ○ Dus \(P\kern{-.8pt}R≈23{,}3\text{.}\) 1p |
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Tangens (2)
007n - Sinus, cosinus en tangens - basis - 0ms
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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 Gegeven is \(\triangle K\kern{-.8pt}L\kern{-.8pt}M\) met \(K\kern{-.8pt}L=39\text{,}\) \(\angle M=59\degree\) en \(\angle K=90\degree\text{.}\) |
○ Tangens in \(\triangle K\kern{-.8pt}L\kern{-.8pt}M\) geeft \(\tan(\angle M)={K\kern{-.8pt}L \over K\kern{-.8pt}M}\) ofwel \(\tan(59\degree)={39 \over K\kern{-.8pt}M}\text{.}\) 1p ○ Hieruit volgt \(K\kern{-.8pt}M={39 \over \tan(59\degree)}\text{.}\) 1p ○ Dus \(K\kern{-.8pt}M≈23{,}4\text{.}\) 1p |
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Tangens (3)
007o - Sinus, cosinus en tangens - basis - 0ms
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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 Gegeven is \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) met \(A\kern{-.8pt}C=56\text{,}\) \(A\kern{-.8pt}B=44\) en \(\angle A=90\degree\text{.}\) |
○ Tangens in \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) geeft \(\tan(\angle C)={A\kern{-.8pt}B \over A\kern{-.8pt}C}\) ofwel \(\tan(\angle C)={44 \over 56}\text{.}\) 1p ○ Hieruit volgt \(\angle C=\tan^{-1}({44 \over 56})\text{.}\) 1p ○ Dus \(\angle C≈38{,}2\degree\text{.}\) 1p |