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 \(B\kern{-.8pt}C = 41 \text{,}\) \(\angle C = 56\degree\) 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 \(\cos(56\degree) = {A\kern{-.8pt}C \over 41} \text{.}\) 1p ○ Hieruit volgt \(A\kern{-.8pt}C = 41 ⋅ \cos(56\degree) \text{.}\) 1p ○ Dus \(A\kern{-.8pt}C ≈ 22{,}9 \text{.}\) 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 \(L\kern{-.8pt}M = 44 \text{,}\) \(\angle L = 47\degree\) 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 \(\cos(47\degree) = {44 \over K\kern{-.8pt}L} \text{.}\) 1p ○ Hieruit volgt \(K\kern{-.8pt}L = {44 \over \cos(47\degree)} \text{.}\) 1p ○ Dus \(K\kern{-.8pt}L ≈ 64{,}5 \text{.}\) 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 \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) met \(Q\kern{-.8pt}R = 55 \text{,}\) \(P\kern{-.8pt}Q = 66\) 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 \(\cos(\angle Q) = {55 \over 66} \text{.}\) 1p ○ Hieruit volgt \(\angle Q = \cos^{-1}({55 \over 66}) \text{.}\) 1p ○ Dus \(\angle Q ≈ 33{,}6\degree \text{.}\) 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 \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) met \(Q\kern{-.8pt}R = 43 \text{,}\) \(\angle R = 43\degree\) 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 \(\sin(43\degree) = {P\kern{-.8pt}Q \over 43} \text{.}\) 1p ○ Hieruit volgt \(P\kern{-.8pt}Q = 43 ⋅ \sin(43\degree) \text{.}\) 1p ○ Dus \(P\kern{-.8pt}Q ≈ 29{,}3 \text{.}\) 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 \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) met \(A\kern{-.8pt}B = 30 \text{,}\) \(\angle C = 47\degree\) 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 \(\sin(47\degree) = {30 \over B\kern{-.8pt}C} \text{.}\) 1p ○ Hieruit volgt \(B\kern{-.8pt}C = {30 \over \sin(47\degree)} \text{.}\) 1p ○ Dus \(B\kern{-.8pt}C ≈ 41{,}0 \text{.}\) 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 \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) met \(A\kern{-.8pt}B = 24 \text{,}\) \(B\kern{-.8pt}C = 52\) 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 \(\sin(\angle C) = {24 \over 52} \text{.}\) 1p ○ Hieruit volgt \(\angle C = \sin^{-1}({24 \over 52}) \text{.}\) 1p ○ Dus \(\angle C ≈ 27{,}5\degree \text{.}\) 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 \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) met \(A\kern{-.8pt}C = 35 \text{,}\) \(\angle C = 57\degree\) 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 \(\tan(57\degree) = {A\kern{-.8pt}B \over 35} \text{.}\) 1p ○ Hieruit volgt \(A\kern{-.8pt}B = 35 ⋅ \tan(57\degree) \text{.}\) 1p ○ Dus \(A\kern{-.8pt}B ≈ 53{,}9 \text{.}\) 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 \(L\kern{-.8pt}M = 33 \text{,}\) \(\angle K = 34\degree\) 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 \(\tan(34\degree) = {33 \over K\kern{-.8pt}L} \text{.}\) 1p ○ Hieruit volgt \(K\kern{-.8pt}L = {33 \over \tan(34\degree)} \text{.}\) 1p ○ Dus \(K\kern{-.8pt}L ≈ 48{,}9 \text{.}\) 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 \(L\kern{-.8pt}M = 24 \text{,}\) \(K\kern{-.8pt}M = 54\) en \(\angle M = 90\degree \text{.}\) |
○ Tangens in \(\triangle K\kern{-.8pt}L\kern{-.8pt}M\) geeft \(\tan(\angle L) = {K\kern{-.8pt}M \over L\kern{-.8pt}M}\) ofwel \(\tan(\angle L) = {54 \over 24} \text{.}\) 1p ○ Hieruit volgt \(\angle L = \tan^{-1}({54 \over 24}) \text{.}\) 1p ○ Dus \(\angle L ≈ 66{,}0\degree \text{.}\) 1p |