Sinus, cosinus en tangens
14 - 9 oefeningen
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Cosinus (1)
007j - basis
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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 a Gegeven is \(\triangle KLM\) met \(KM=40\text{,}\) \(\angle K=38\degree\) en \(\angle L=90\degree\text{.}\) |
a Cosinus in \(\triangle KLM\) geeft \(\cos(\angle K)={KL \over KM}\) ofwel \(\cos(38\degree)={KL \over 40}\text{.}\) 1p Hieruit volgt \(KL=40⋅\cos(38\degree)\text{.}\) 1p Dus \(KL≈31{,}5\text{.}\) 1p |
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Cosinus (2)
007k - basis
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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 a Gegeven is \(\triangle PQR\) met \(PR=25\text{,}\) \(\angle R=43\degree\) en \(\angle P=90\degree\text{.}\) |
a Cosinus in \(\triangle PQR\) geeft \(\cos(\angle R)={PR \over QR}\) ofwel \(\cos(43\degree)={25 \over QR}\text{.}\) 1p Hieruit volgt \(QR={25 \over \cos(43\degree)}\text{.}\) 1p Dus \(QR≈34{,}2\text{.}\) 1p |
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Cosinus (3)
007l - basis
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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 a Gegeven is \(\triangle KLM\) met \(LM=57\text{,}\) \(KL=69\) en \(\angle M=90\degree\text{.}\) |
a Cosinus in \(\triangle KLM\) geeft \(\cos(\angle L)={LM \over KL}\) ofwel \(\cos(\angle L)={57 \over 69}\text{.}\) 1p Hieruit volgt \(\angle L=\cos^{-1}({57 \over 69})\text{.}\) 1p Dus \(\angle L≈34{,}3\degree\text{.}\) 1p |
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Sinus (1)
007g - basis
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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 a Gegeven is \(\triangle PQR\) met \(QR=74\text{,}\) \(\angle R=38\degree\) en \(\angle P=90\degree\text{.}\) |
a Sinus in \(\triangle PQR\) geeft \(\sin(\angle R)={PQ \over QR}\) ofwel \(\sin(38\degree)={PQ \over 74}\text{.}\) 1p Hieruit volgt \(PQ=74⋅\sin(38\degree)\text{.}\) 1p Dus \(PQ≈45{,}6\text{.}\) 1p |
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Sinus (2)
007h - basis
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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 a Gegeven is \(\triangle PQR\) met \(PR=33\text{,}\) \(\angle Q=35\degree\) en \(\angle R=90\degree\text{.}\) |
a Sinus in \(\triangle PQR\) geeft \(\sin(\angle Q)={PR \over PQ}\) ofwel \(\sin(35\degree)={33 \over PQ}\text{.}\) 1p Hieruit volgt \(PQ={33 \over \sin(35\degree)}\text{.}\) 1p Dus \(PQ≈57{,}5\text{.}\) 1p |
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Sinus (3)
007i - basis
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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 a Gegeven is \(\triangle ABC\) met \(BC=49\text{,}\) \(AC=69\) en \(\angle B=90\degree\text{.}\) |
a Sinus in \(\triangle ABC\) geeft \(\sin(\angle A)={BC \over AC}\) ofwel \(\sin(\angle A)={49 \over 69}\text{.}\) 1p Hieruit volgt \(\angle A=\sin^{-1}({49 \over 69})\text{.}\) 1p Dus \(\angle A≈45{,}2\degree\text{.}\) 1p |
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Tangens (1)
007m - basis
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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 a Gegeven is \(\triangle ABC\) met \(AB=53\text{,}\) \(\angle A=58\degree\) en \(\angle B=90\degree\text{.}\) |
a Tangens in \(\triangle ABC\) geeft \(\tan(\angle A)={BC \over AB}\) ofwel \(\tan(58\degree)={BC \over 53}\text{.}\) 1p Hieruit volgt \(BC=53⋅\tan(58\degree)\text{.}\) 1p Dus \(BC≈84{,}8\text{.}\) 1p |
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Tangens (2)
007n - basis
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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 a Gegeven is \(\triangle KLM\) met \(KL=59\text{,}\) \(\angle M=47\degree\) en \(\angle K=90\degree\text{.}\) |
a Tangens in \(\triangle KLM\) geeft \(\tan(\angle M)={KL \over KM}\) ofwel \(\tan(47\degree)={59 \over KM}\text{.}\) 1p Hieruit volgt \(KM={59 \over \tan(47\degree)}\text{.}\) 1p Dus \(KM≈55{,}0\text{.}\) 1p |
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Tangens (3)
007o - basis
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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 a Gegeven is \(\triangle ABC\) met \(BC=29\text{,}\) \(AC=26\) en \(\angle C=90\degree\text{.}\) |
a Tangens in \(\triangle ABC\) geeft \(\tan(\angle B)={AC \over BC}\) ofwel \(\tan(\angle B)={26 \over 29}\text{.}\) 1p Hieruit volgt \(\angle B=\tan^{-1}({26 \over 29})\text{.}\) 1p Dus \(\angle B≈41{,}9\degree\text{.}\) 1p |