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 \(P\kern{-.8pt}Q = 61 \text{,}\) \(\angle Q = 54\degree\) 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 \(\cos(54\degree) = {Q\kern{-.8pt}R \over 61} \text{.}\) 1p ○ Hieruit volgt \(Q\kern{-.8pt}R = 61 ⋅ \cos(54\degree) \text{.}\) 1p ○ Dus \(Q\kern{-.8pt}R ≈ 35{,}9 \text{.}\) 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 \(K\kern{-.8pt}M = 31 \text{,}\) \(\angle M = 35\degree\) en \(\angle K = 90\degree \text{.}\) |
○ Cosinus in \(\triangle K\kern{-.8pt}L\kern{-.8pt}M\) geeft \(\cos(\angle M) = {K\kern{-.8pt}M \over L\kern{-.8pt}M}\) ofwel \(\cos(35\degree) = {31 \over L\kern{-.8pt}M} \text{.}\) 1p ○ Hieruit volgt \(L\kern{-.8pt}M = {31 \over \cos(35\degree)} \text{.}\) 1p ○ Dus \(L\kern{-.8pt}M ≈ 37{,}8 \text{.}\) 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 \(\triangle K\kern{-.8pt}L\kern{-.8pt}M\) met \(L\kern{-.8pt}M = 36 \text{,}\) \(K\kern{-.8pt}L = 43\) 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 \(\cos(\angle L) = {36 \over 43} \text{.}\) 1p ○ Hieruit volgt \(\angle L = \cos^{-1}({36 \over 43}) \text{.}\) 1p ○ Dus \(\angle L ≈ 33{,}2\degree \text{.}\) 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 \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) met \(Q\kern{-.8pt}R = 44 \text{,}\) \(\angle R = 48\degree\) 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 \(\sin(48\degree) = {P\kern{-.8pt}Q \over 44} \text{.}\) 1p ○ Hieruit volgt \(P\kern{-.8pt}Q = 44 ⋅ \sin(48\degree) \text{.}\) 1p ○ Dus \(P\kern{-.8pt}Q ≈ 32{,}7 \text{.}\) 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 \(A\kern{-.8pt}B = 58 \text{,}\) \(\angle C = 55\degree\) 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 \(\sin(55\degree) = {58 \over B\kern{-.8pt}C} \text{.}\) 1p ○ Hieruit volgt \(B\kern{-.8pt}C = {58 \over \sin(55\degree)} \text{.}\) 1p ○ Dus \(B\kern{-.8pt}C ≈ 70{,}8 \text{.}\) 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 \(\triangle K\kern{-.8pt}L\kern{-.8pt}M\) met \(L\kern{-.8pt}M = 47 \text{,}\) \(K\kern{-.8pt}M = 76\) 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 \(\sin(\angle K) = {47 \over 76} \text{.}\) 1p ○ Hieruit volgt \(\angle K = \sin^{-1}({47 \over 76}) \text{.}\) 1p ○ Dus \(\angle K ≈ 38{,}2\degree \text{.}\) 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 \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) met \(Q\kern{-.8pt}R = 36 \text{,}\) \(\angle Q = 48\degree\) 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 \(\tan(48\degree) = {P\kern{-.8pt}R \over 36} \text{.}\) 1p ○ Hieruit volgt \(P\kern{-.8pt}R = 36 ⋅ \tan(48\degree) \text{.}\) 1p ○ Dus \(P\kern{-.8pt}R ≈ 40{,}0 \text{.}\) 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 \(P\kern{-.8pt}R = 22 \text{,}\) \(\angle Q = 54\degree\) 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 \(\tan(54\degree) = {22 \over Q\kern{-.8pt}R} \text{.}\) 1p ○ Hieruit volgt \(Q\kern{-.8pt}R = {22 \over \tan(54\degree)} \text{.}\) 1p ○ Dus \(Q\kern{-.8pt}R ≈ 16{,}0 \text{.}\) 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 \(A\kern{-.8pt}C = 49 \text{,}\) \(A\kern{-.8pt}B = 51\) 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 \(\tan(\angle C) = {51 \over 49} \text{.}\) 1p ○ Hieruit volgt \(\angle C = \tan^{-1}({51 \over 49}) \text{.}\) 1p ○ Dus \(\angle C ≈ 46{,}1\degree \text{.}\) 1p |