Sinus, cosinus en tangens
14 - 9 oefeningen
|
Cosinus (1)
007j - Sinus, cosinus en tangens - basis - 0ms
|
Getal & Ruimte (13e editie) - 3 havo - 6.4 Getal & Ruimte (13e editie) - 3 vwo - 6.4 |
|
3p Gegeven is \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) met \(A\kern{-.8pt}C = 47 \text{,}\) \(\angle A = 43\degree\) 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 \(\cos(43\degree) = {A\kern{-.8pt}B \over 47} \text{.}\) 1p ○ Hieruit volgt \(A\kern{-.8pt}B = 47 ⋅ \cos(43\degree) \text{.}\) 1p ○ Dus \(A\kern{-.8pt}B ≈ 34{,}4 \text{.}\) 1p |
|
Cosinus (2)
007k - Sinus, cosinus en tangens - basis - 0ms
|
Getal & Ruimte (13e editie) - 3 havo - 6.4 Getal & Ruimte (13e editie) - 3 vwo - 6.4 |
|
3p Gegeven is \(\triangle K\kern{-.8pt}L\kern{-.8pt}M\) met \(L\kern{-.8pt}M = 21 \text{,}\) \(\angle L = 40\degree\) 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 \(\cos(40\degree) = {21 \over K\kern{-.8pt}L} \text{.}\) 1p ○ Hieruit volgt \(K\kern{-.8pt}L = {21 \over \cos(40\degree)} \text{.}\) 1p ○ Dus \(K\kern{-.8pt}L ≈ 27{,}4 \text{.}\) 1p |
|
Cosinus (3)
007l - Sinus, cosinus en tangens - basis - 0ms
|
Getal & Ruimte (13e editie) - 3 havo - 6.4 Getal & Ruimte (13e editie) - 3 vwo - 6.4 |
|
3p Gegeven is \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) met \(A\kern{-.8pt}C = 24 \text{,}\) \(B\kern{-.8pt}C = 35\) 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 \(\cos(\angle C) = {24 \over 35} \text{.}\) 1p ○ Hieruit volgt \(\angle C = \cos^{-1}({24 \over 35}) \text{.}\) 1p ○ Dus \(\angle C ≈ 46{,}7\degree \text{.}\) 1p |
|
Sinus (1)
007g - Sinus, cosinus en tangens - basis - 0ms
|
Getal & Ruimte (13e editie) - 3 havo - 6.4 Getal & Ruimte (13e editie) - 3 vwo - 6.4 |
|
3p Gegeven is \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) met \(P\kern{-.8pt}Q = 43 \text{,}\) \(\angle Q = 58\degree\) 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 \(\sin(58\degree) = {P\kern{-.8pt}R \over 43} \text{.}\) 1p ○ Hieruit volgt \(P\kern{-.8pt}R = 43 ⋅ \sin(58\degree) \text{.}\) 1p ○ Dus \(P\kern{-.8pt}R ≈ 36{,}5 \text{.}\) 1p |
|
Sinus (2)
007h - Sinus, cosinus en tangens - basis - 0ms
|
Getal & Ruimte (13e editie) - 3 havo - 6.4 Getal & Ruimte (13e editie) - 3 vwo - 6.4 |
|
3p Gegeven is \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) met \(Q\kern{-.8pt}R = 29 \text{,}\) \(\angle P = 59\degree\) en \(\angle Q = 90\degree \text{.}\) |
○ Sinus in \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) geeft \(\sin(\angle P) = {Q\kern{-.8pt}R \over P\kern{-.8pt}R}\) ofwel \(\sin(59\degree) = {29 \over P\kern{-.8pt}R} \text{.}\) 1p ○ Hieruit volgt \(P\kern{-.8pt}R = {29 \over \sin(59\degree)} \text{.}\) 1p ○ Dus \(P\kern{-.8pt}R ≈ 33{,}8 \text{.}\) 1p |
|
Sinus (3)
007i - Sinus, cosinus en tangens - basis - 0ms
|
Getal & Ruimte (13e editie) - 3 havo - 6.4 Getal & Ruimte (13e editie) - 3 vwo - 6.4 |
|
3p Gegeven is \(\triangle K\kern{-.8pt}L\kern{-.8pt}M\) met \(K\kern{-.8pt}L = 33 \text{,}\) \(L\kern{-.8pt}M = 46\) 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 \(\sin(\angle M) = {33 \over 46} \text{.}\) 1p ○ Hieruit volgt \(\angle M = \sin^{-1}({33 \over 46}) \text{.}\) 1p ○ Dus \(\angle M ≈ 45{,}8\degree \text{.}\) 1p |
|
Tangens (1)
007m - Sinus, cosinus en tangens - basis - 0ms
|
Getal & Ruimte (13e editie) - 3 havo - 6.3 Getal & Ruimte (13e editie) - 3 vwo - 6.3 |
|
3p Gegeven is \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) met \(B\kern{-.8pt}C = 52 \text{,}\) \(\angle B = 48\degree\) 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 \(\tan(48\degree) = {A\kern{-.8pt}C \over 52} \text{.}\) 1p ○ Hieruit volgt \(A\kern{-.8pt}C = 52 ⋅ \tan(48\degree) \text{.}\) 1p ○ Dus \(A\kern{-.8pt}C ≈ 57{,}8 \text{.}\) 1p |
|
Tangens (2)
007n - Sinus, cosinus en tangens - basis - 0ms
|
Getal & Ruimte (13e editie) - 3 havo - 6.3 Getal & Ruimte (13e editie) - 3 vwo - 6.3 |
|
3p Gegeven is \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) met \(B\kern{-.8pt}C = 29 \text{,}\) \(\angle A = 36\degree\) 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 \(\tan(36\degree) = {29 \over A\kern{-.8pt}B} \text{.}\) 1p ○ Hieruit volgt \(A\kern{-.8pt}B = {29 \over \tan(36\degree)} \text{.}\) 1p ○ Dus \(A\kern{-.8pt}B ≈ 39{,}9 \text{.}\) 1p |
|
Tangens (3)
007o - Sinus, cosinus en tangens - basis - 0ms
|
Getal & Ruimte (13e editie) - 3 havo - 6.3 Getal & Ruimte (13e editie) - 3 vwo - 6.3 |
|
3p Gegeven is \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) met \(P\kern{-.8pt}R = 40 \text{,}\) \(P\kern{-.8pt}Q = 41\) en \(\angle P = 90\degree \text{.}\) |
○ Tangens in \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) geeft \(\tan(\angle R) = {P\kern{-.8pt}Q \over P\kern{-.8pt}R}\) ofwel \(\tan(\angle R) = {41 \over 40} \text{.}\) 1p ○ Hieruit volgt \(\angle R = \tan^{-1}({41 \over 40}) \text{.}\) 1p ○ Dus \(\angle R ≈ 45{,}7\degree \text{.}\) 1p |