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 \(Q\kern{-.8pt}R = 42 \text{,}\) \(\angle R = 43\degree\) en \(\angle P = 90\degree \text{.}\) |
○ Cosinus in \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) geeft \(\cos(\angle R) = {P\kern{-.8pt}R \over Q\kern{-.8pt}R}\) ofwel \(\cos(43\degree) = {P\kern{-.8pt}R \over 42} \text{.}\) 1p ○ Hieruit volgt \(P\kern{-.8pt}R = 42 ⋅ \cos(43\degree) \text{.}\) 1p ○ Dus \(P\kern{-.8pt}R ≈ 30{,}7 \text{.}\) 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 \(A\kern{-.8pt}B = 21 \text{,}\) \(\angle A = 47\degree\) 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 \(\cos(47\degree) = {21 \over A\kern{-.8pt}C} \text{.}\) 1p ○ Hieruit volgt \(A\kern{-.8pt}C = {21 \over \cos(47\degree)} \text{.}\) 1p ○ Dus \(A\kern{-.8pt}C ≈ 30{,}8 \text{.}\) 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 \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) met \(B\kern{-.8pt}C = 47 \text{,}\) \(A\kern{-.8pt}B = 51\) 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 \(\cos(\angle B) = {47 \over 51} \text{.}\) 1p ○ Hieruit volgt \(\angle B = \cos^{-1}({47 \over 51}) \text{.}\) 1p ○ Dus \(\angle B ≈ 22{,}8\degree \text{.}\) 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 \(Q\kern{-.8pt}R = 48 \text{,}\) \(\angle R = 50\degree\) 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 \(\sin(50\degree) = {P\kern{-.8pt}Q \over 48} \text{.}\) 1p ○ Hieruit volgt \(P\kern{-.8pt}Q = 48 ⋅ \sin(50\degree) \text{.}\) 1p ○ Dus \(P\kern{-.8pt}Q ≈ 36{,}8 \text{.}\) 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 \(K\kern{-.8pt}M = 34 \text{,}\) \(\angle L = 51\degree\) 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 \(\sin(51\degree) = {34 \over K\kern{-.8pt}L} \text{.}\) 1p ○ Hieruit volgt \(K\kern{-.8pt}L = {34 \over \sin(51\degree)} \text{.}\) 1p ○ Dus \(K\kern{-.8pt}L ≈ 43{,}7 \text{.}\) 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 \(A\kern{-.8pt}C = 47 \text{,}\) \(A\kern{-.8pt}B = 64\) en \(\angle C = 90\degree \text{.}\) |
○ Sinus in \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) geeft \(\sin(\angle B) = {A\kern{-.8pt}C \over A\kern{-.8pt}B}\) ofwel \(\sin(\angle B) = {47 \over 64} \text{.}\) 1p ○ Hieruit volgt \(\angle B = \sin^{-1}({47 \over 64}) \text{.}\) 1p ○ Dus \(\angle B ≈ 47{,}3\degree \text{.}\) 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 \(B\kern{-.8pt}C = 42 \text{,}\) \(\angle B = 32\degree\) 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 \(\tan(32\degree) = {A\kern{-.8pt}C \over 42} \text{.}\) 1p ○ Hieruit volgt \(A\kern{-.8pt}C = 42 ⋅ \tan(32\degree) \text{.}\) 1p ○ Dus \(A\kern{-.8pt}C ≈ 26{,}2 \text{.}\) 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 \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) met \(A\kern{-.8pt}C = 47 \text{,}\) \(\angle B = 32\degree\) 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 \(\tan(32\degree) = {47 \over B\kern{-.8pt}C} \text{.}\) 1p ○ Hieruit volgt \(B\kern{-.8pt}C = {47 \over \tan(32\degree)} \text{.}\) 1p ○ Dus \(B\kern{-.8pt}C ≈ 75{,}2 \text{.}\) 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 \(A\kern{-.8pt}B = 29 \text{,}\) \(B\kern{-.8pt}C = 23\) 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 \(\tan(\angle A) = {23 \over 29} \text{.}\) 1p ○ Hieruit volgt \(\angle A = \tan^{-1}({23 \over 29}) \text{.}\) 1p ○ Dus \(\angle A ≈ 38{,}4\degree \text{.}\) 1p |