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 \(P\kern{-.8pt}R = 68 \text{,}\) \(\angle P = 34\degree\) en \(\angle Q = 90\degree \text{.}\) |
○ Cosinus in \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) geeft \(\cos(\angle P) = {P\kern{-.8pt}Q \over P\kern{-.8pt}R}\) ofwel \(\cos(34\degree) = {P\kern{-.8pt}Q \over 68} \text{.}\) 1p ○ Hieruit volgt \(P\kern{-.8pt}Q = 68 ⋅ \cos(34\degree) \text{.}\) 1p ○ Dus \(P\kern{-.8pt}Q ≈ 56{,}4 \text{.}\) 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 \(A\kern{-.8pt}C = 37 \text{,}\) \(\angle C = 54\degree\) 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 \(\cos(54\degree) = {37 \over B\kern{-.8pt}C} \text{.}\) 1p ○ Hieruit volgt \(B\kern{-.8pt}C = {37 \over \cos(54\degree)} \text{.}\) 1p ○ Dus \(B\kern{-.8pt}C ≈ 62{,}9 \text{.}\) 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 \(B\kern{-.8pt}C = 55 \text{,}\) \(A\kern{-.8pt}B = 66\) 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 \(\cos(\angle B) = {55 \over 66} \text{.}\) 1p ○ Hieruit volgt \(\angle B = \cos^{-1}({55 \over 66}) \text{.}\) 1p ○ Dus \(\angle B ≈ 33{,}6\degree \text{.}\) 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 \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) met \(A\kern{-.8pt}C = 66 \text{,}\) \(\angle A = 31\degree\) en \(\angle B = 90\degree \text{.}\) |
○ Sinus in \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) geeft \(\sin(\angle A) = {B\kern{-.8pt}C \over A\kern{-.8pt}C}\) ofwel \(\sin(31\degree) = {B\kern{-.8pt}C \over 66} \text{.}\) 1p ○ Hieruit volgt \(B\kern{-.8pt}C = 66 ⋅ \sin(31\degree) \text{.}\) 1p ○ Dus \(B\kern{-.8pt}C ≈ 34{,}0 \text{.}\) 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 \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) met \(P\kern{-.8pt}R = 51 \text{,}\) \(\angle Q = 39\degree\) en \(\angle R = 90\degree \text{.}\) |
○ Sinus in \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) geeft \(\sin(\angle Q) = {P\kern{-.8pt}R \over P\kern{-.8pt}Q}\) ofwel \(\sin(39\degree) = {51 \over P\kern{-.8pt}Q} \text{.}\) 1p ○ Hieruit volgt \(P\kern{-.8pt}Q = {51 \over \sin(39\degree)} \text{.}\) 1p ○ Dus \(P\kern{-.8pt}Q ≈ 81{,}0 \text{.}\) 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 \(A\kern{-.8pt}B = 27 \text{,}\) \(B\kern{-.8pt}C = 40\) 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 \(\sin(\angle C) = {27 \over 40} \text{.}\) 1p ○ Hieruit volgt \(\angle C = \sin^{-1}({27 \over 40}) \text{.}\) 1p ○ Dus \(\angle C ≈ 42{,}5\degree \text{.}\) 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 \(L\kern{-.8pt}M = 54 \text{,}\) \(\angle L = 40\degree\) 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 \(\tan(40\degree) = {K\kern{-.8pt}M \over 54} \text{.}\) 1p ○ Hieruit volgt \(K\kern{-.8pt}M = 54 ⋅ \tan(40\degree) \text{.}\) 1p ○ Dus \(K\kern{-.8pt}M ≈ 45{,}3 \text{.}\) 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 \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) met \(A\kern{-.8pt}B = 53 \text{,}\) \(\angle C = 58\degree\) 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 \(\tan(58\degree) = {53 \over A\kern{-.8pt}C} \text{.}\) 1p ○ Hieruit volgt \(A\kern{-.8pt}C = {53 \over \tan(58\degree)} \text{.}\) 1p ○ Dus \(A\kern{-.8pt}C ≈ 33{,}1 \text{.}\) 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 \(A\kern{-.8pt}B = 30 \text{,}\) \(B\kern{-.8pt}C = 41\) en \(\angle B = 90\degree \text{.}\) |
○ Tangens in \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) geeft \(\tan(\angle A) = {B\kern{-.8pt}C \over A\kern{-.8pt}B}\) ofwel \(\tan(\angle A) = {41 \over 30} \text{.}\) 1p ○ Hieruit volgt \(\angle A = \tan^{-1}({41 \over 30}) \text{.}\) 1p ○ Dus \(\angle A ≈ 53{,}8\degree \text{.}\) 1p |