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 \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) met \(P\kern{-.8pt}Q = 43 \text{,}\) \(\angle Q = 35\degree\) en \(\angle R = 90\degree \text{.}\) |
○ Cosinus in \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) geeft \(\cos(\angle Q) = {Q\kern{-.8pt}R \over P\kern{-.8pt}Q}\) ofwel \(\cos(35\degree) = {Q\kern{-.8pt}R \over 43} \text{.}\) 1p ○ Hieruit volgt \(Q\kern{-.8pt}R = 43 ⋅ \cos(35\degree) \text{.}\) 1p ○ Dus \(Q\kern{-.8pt}R ≈ 35{,}2 \text{.}\) 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 \(\triangle K\kern{-.8pt}L\kern{-.8pt}M\) met \(L\kern{-.8pt}M = 33 \text{,}\) \(\angle L = 38\degree\) en \(\angle M = 90\degree \text{.}\) |
○ Cosinus in \(\triangle K\kern{-.8pt}L\kern{-.8pt}M\) geeft \(\cos(\angle L) = {L\kern{-.8pt}M \over K\kern{-.8pt}L}\) ofwel \(\cos(38\degree) = {33 \over K\kern{-.8pt}L} \text{.}\) 1p ○ Hieruit volgt \(K\kern{-.8pt}L = {33 \over \cos(38\degree)} \text{.}\) 1p ○ Dus \(K\kern{-.8pt}L ≈ 41{,}9 \text{.}\) 1p |
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Cosinus (3)
007l - 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 \(B\kern{-.8pt}C = 41 \text{,}\) \(A\kern{-.8pt}B = 47\) 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 \(\cos(\angle B) = {41 \over 47} \text{.}\) 1p ○ Hieruit volgt \(\angle B = \cos^{-1}({41 \over 47}) \text{.}\) 1p ○ Dus \(\angle B ≈ 29{,}3\degree \text{.}\) 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 \(K\kern{-.8pt}M = 78 \text{,}\) \(\angle K = 32\degree\) en \(\angle L = 90\degree \text{.}\) |
○ Sinus in \(\triangle K\kern{-.8pt}L\kern{-.8pt}M\) geeft \(\sin(\angle K) = {L\kern{-.8pt}M \over K\kern{-.8pt}M}\) ofwel \(\sin(32\degree) = {L\kern{-.8pt}M \over 78} \text{.}\) 1p ○ Hieruit volgt \(L\kern{-.8pt}M = 78 ⋅ \sin(32\degree) \text{.}\) 1p ○ Dus \(L\kern{-.8pt}M ≈ 41{,}3 \text{.}\) 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 \(\triangle K\kern{-.8pt}L\kern{-.8pt}M\) met \(K\kern{-.8pt}M = 29 \text{,}\) \(\angle L = 40\degree\) 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 \(\sin(40\degree) = {29 \over K\kern{-.8pt}L} \text{.}\) 1p ○ Hieruit volgt \(K\kern{-.8pt}L = {29 \over \sin(40\degree)} \text{.}\) 1p ○ Dus \(K\kern{-.8pt}L ≈ 45{,}1 \text{.}\) 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 \(Q\kern{-.8pt}R = 27 \text{,}\) \(P\kern{-.8pt}R = 48\) en \(\angle Q = 90\degree \text{.}\) |
○ Sinus in \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) geeft \(\sin(\angle P) = {Q\kern{-.8pt}R \over P\kern{-.8pt}R}\) ofwel \(\sin(\angle P) = {27 \over 48} \text{.}\) 1p ○ Hieruit volgt \(\angle P = \sin^{-1}({27 \over 48}) \text{.}\) 1p ○ Dus \(\angle P ≈ 34{,}2\degree \text{.}\) 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 \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) met \(B\kern{-.8pt}C = 51 \text{,}\) \(\angle B = 48\degree\) en \(\angle C = 90\degree \text{.}\) |
○ Tangens in \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) geeft \(\tan(\angle B) = {A\kern{-.8pt}C \over B\kern{-.8pt}C}\) ofwel \(\tan(48\degree) = {A\kern{-.8pt}C \over 51} \text{.}\) 1p ○ Hieruit volgt \(A\kern{-.8pt}C = 51 ⋅ \tan(48\degree) \text{.}\) 1p ○ Dus \(A\kern{-.8pt}C ≈ 56{,}6 \text{.}\) 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 \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) met \(Q\kern{-.8pt}R = 60 \text{,}\) \(\angle P = 40\degree\) en \(\angle Q = 90\degree \text{.}\) |
○ Tangens in \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) geeft \(\tan(\angle P) = {Q\kern{-.8pt}R \over P\kern{-.8pt}Q}\) ofwel \(\tan(40\degree) = {60 \over P\kern{-.8pt}Q} \text{.}\) 1p ○ Hieruit volgt \(P\kern{-.8pt}Q = {60 \over \tan(40\degree)} \text{.}\) 1p ○ Dus \(P\kern{-.8pt}Q ≈ 71{,}5 \text{.}\) 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 \(A\kern{-.8pt}C = 60 \text{,}\) \(A\kern{-.8pt}B = 47\) 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 \(\tan(\angle C) = {47 \over 60} \text{.}\) 1p ○ Hieruit volgt \(\angle C = \tan^{-1}({47 \over 60}) \text{.}\) 1p ○ Dus \(\angle C ≈ 38{,}1\degree \text{.}\) 1p |