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 \(A\kern{-.8pt}C = 80 \text{,}\) \(\angle A = 56\degree\) 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 \(\cos(56\degree) = {A\kern{-.8pt}B \over 80} \text{.}\) 1p ○ Hieruit volgt \(A\kern{-.8pt}B = 80 ⋅ \cos(56\degree) \text{.}\) 1p ○ Dus \(A\kern{-.8pt}B ≈ 44{,}7 \text{.}\) 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 \(A\kern{-.8pt}C = 46 \text{,}\) \(\angle C = 54\degree\) 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 \(\cos(54\degree) = {46 \over B\kern{-.8pt}C} \text{.}\) 1p ○ Hieruit volgt \(B\kern{-.8pt}C = {46 \over \cos(54\degree)} \text{.}\) 1p ○ Dus \(B\kern{-.8pt}C ≈ 78{,}3 \text{.}\) 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 \(A\kern{-.8pt}B = 39 \text{,}\) \(A\kern{-.8pt}C = 51\) 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 \(\cos(\angle A) = {39 \over 51} \text{.}\) 1p ○ Hieruit volgt \(\angle A = \cos^{-1}({39 \over 51}) \text{.}\) 1p ○ Dus \(\angle A ≈ 40{,}1\degree \text{.}\) 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 \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) met \(B\kern{-.8pt}C = 69 \text{,}\) \(\angle C = 52\degree\) 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 \(\sin(52\degree) = {A\kern{-.8pt}B \over 69} \text{.}\) 1p ○ Hieruit volgt \(A\kern{-.8pt}B = 69 ⋅ \sin(52\degree) \text{.}\) 1p ○ Dus \(A\kern{-.8pt}B ≈ 54{,}4 \text{.}\) 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 \(L\kern{-.8pt}M = 45 \text{,}\) \(\angle K = 39\degree\) 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 \(\sin(39\degree) = {45 \over K\kern{-.8pt}M} \text{.}\) 1p ○ Hieruit volgt \(K\kern{-.8pt}M = {45 \over \sin(39\degree)} \text{.}\) 1p ○ Dus \(K\kern{-.8pt}M ≈ 71{,}5 \text{.}\) 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 \(K\kern{-.8pt}L = 59 \text{,}\) \(L\kern{-.8pt}M = 80\) en \(\angle K = 90\degree \text{.}\) |
○ Sinus in \(\triangle K\kern{-.8pt}L\kern{-.8pt}M\) geeft \(\sin(\angle M) = {K\kern{-.8pt}L \over L\kern{-.8pt}M}\) ofwel \(\sin(\angle M) = {59 \over 80} \text{.}\) 1p ○ Hieruit volgt \(\angle M = \sin^{-1}({59 \over 80}) \text{.}\) 1p ○ Dus \(\angle M ≈ 47{,}5\degree \text{.}\) 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 \(\triangle K\kern{-.8pt}L\kern{-.8pt}M\) met \(K\kern{-.8pt}M = 27 \text{,}\) \(\angle M = 34\degree\) 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 \(\tan(34\degree) = {K\kern{-.8pt}L \over 27} \text{.}\) 1p ○ Hieruit volgt \(K\kern{-.8pt}L = 27 ⋅ \tan(34\degree) \text{.}\) 1p ○ Dus \(K\kern{-.8pt}L ≈ 18{,}2 \text{.}\) 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 \(K\kern{-.8pt}L = 33 \text{,}\) \(\angle M = 41\degree\) 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 \(\tan(41\degree) = {33 \over K\kern{-.8pt}M} \text{.}\) 1p ○ Hieruit volgt \(K\kern{-.8pt}M = {33 \over \tan(41\degree)} \text{.}\) 1p ○ Dus \(K\kern{-.8pt}M ≈ 38{,}0 \text{.}\) 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 \(\triangle K\kern{-.8pt}L\kern{-.8pt}M\) met \(K\kern{-.8pt}L = 49 \text{,}\) \(L\kern{-.8pt}M = 47\) en \(\angle L = 90\degree \text{.}\) |
○ Tangens in \(\triangle K\kern{-.8pt}L\kern{-.8pt}M\) geeft \(\tan(\angle K) = {L\kern{-.8pt}M \over K\kern{-.8pt}L}\) ofwel \(\tan(\angle K) = {47 \over 49} \text{.}\) 1p ○ Hieruit volgt \(\angle K = \tan^{-1}({47 \over 49}) \text{.}\) 1p ○ Dus \(\angle K ≈ 43{,}8\degree \text{.}\) 1p |