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Gebruik de goniometrische cirkel om de gevraagde waarden af te lezen.

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Lees de waarden van de goniometrische getallen af op de cirkel.

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Lees de waarden van de goniometrische getallen af op de cirkel.

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Gebruik de goniometrische cirkel om de gevraagde waarden af te lezen.

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Gebruik de goniometrische cirkel om de gevraagde waarden af te lezen.

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Lees de waarden van de goniometrische getallen af op de cirkel.

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Gebruik de goniometrische cirkel om de gevraagde waarden af te lezen.

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Lees de waarden van de goniometrische getallen af op de cirkel.

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Als gegeven is dat $\\cos \\alpha = \\displaystyle{\\frac12}$, dan is de hoek $\\displaystyle{\\alpha =- \\frac{\\pi}{3} + 2k\\pi}$ of $\\displaystyle{\\alpha = \\frac{\\pi}{3} + 2k\\pi}$ met $k$ een geheel getal. Geef op deze manier alle oplossingen voor de hoek $\\alpha$ in de volgende gevallen, schrijf telkens die oplossing waarbij $\\alpha$ het kleinst is als $k=0$ eerst. Om $\\pi$ in te geven gebruik je `pi'.

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$\\cos \\alpha = -\\displaystyle{\\frac{1}{2}}$, dan is $\\alpha=$[[0]]$+2k\\pi$ of $\\alpha=$[[1]]$+2k\\pi$ met $k \\in \\mathbb{Z}$.

$\\tan \\alpha = 1$, dan is $\\alpha=$[[0]]$+2k\\pi$ of $\\alpha=$[[1]]$+2k\\pi$ met $k \\in \\mathbb{Z}$.

$\\sin \\alpha = \\displaystyle{\\frac{\\sqrt{3}}{2}}$, dan is $\\alpha=$[[0]]$+2k\\pi$ of $\\alpha=$[[1]]$+2k\\pi$ met $k \\in \\mathbb{Z}$.

$\\cot \\alpha = -1$, dan is $\\alpha=$[[0]]$+2k\\pi$ of $\\alpha=$[[1]]$+2k\\pi$ met $k \\in \\mathbb{Z}$.

$\\cos \\alpha = \\displaystyle{\\frac{\\sqrt{2}}{2}}$, dan is $\\alpha=$[[0]]$+2k\\pi$ of $\\alpha=$[[1]]$+2k\\pi$ met $k \\in \\mathbb{Z}$.

$\\tan \\alpha = -\\displaystyle{\\frac{1}{\\sqrt{3}}}$, dan is $\\alpha=$[[0]]$+2k\\pi$ of $\\alpha=$[[1]]$+2k\\pi$ met $k \\in \\mathbb{Z}$.

$\\sin \\alpha = -\\displaystyle{\\frac{1}{2}}$, dan is $\\alpha=$[[0]]$+2k\\pi$ of $\\alpha=$[[1]]$+2k\\pi$ met $k \\in \\mathbb{Z}$.

$\\cot \\alpha = \\displaystyle{\\sqrt{3}}$, dan is $\\alpha=$[[0]]$+2k\\pi$ of $\\alpha=$[[1]]$+2k\\pi$ met $k \\in \\mathbb{Z}$.

Gegeven is de hoek $\\alpha$ in het eerste kwadrant en $\\sin \\alpha = \\frac{\\var{2a}}{\\var{2a+1}}$. Bereken de andere goniometrische getallen van $\\alpha$.

", "advice": "

Gebruik de grondformule of hoofdeigenschap $ \\cos ^2 \\alpha + \\sin^2 \\alpha = 1$, denk eraan dat $\\alpha$ in het eerste kwadrant zit en dat dus de sinus en de cosinus van $\\alpha$ beide positief zijn en je dus de positieve wortel moeten nemen. Gebruik daarna de definitie van $\\tan \\alpha = \\frac{\\sin \\alpha}{\\cos \\alpha}$ en $\\cot \\alpha = \\frac{\\cos \\alpha}{\\sin \\alpha}$, denk eraan dat delen door een breuk vermenigvuldigen met de omgekeerde breuk is.

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$\\cos \\alpha =$[[0]]

$\\tan \\alpha =$[[1]]

$\\cot \\alpha =$[[2]]

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Gegeven is de hoek $\\alpha$ in het eerste kwadrant en $\\cos \\alpha = \\frac{\\var{2a}}{\\var{2a+1}}$. Bereken de andere goniometrische getallen van $\\alpha$.

", "advice": "

$\\sin \\alpha =$[[0]]

$\\tan \\alpha =$[[1]]

$\\cot \\alpha =$[[2]]

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Gegeven is de hoek $\\alpha$ in het eerste kwadrant en $\\sin \\alpha = \\frac{\\var{2*a+1}}{\\var{3a+2}}$. Bereken de andere goniometrische getallen van $\\alpha$.

", "advice": "

", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(0 .. 2#1)", "description": "", "templateType": "randrange"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "

$\\cos \\alpha =$[[0]]

$\\tan \\alpha =$[[1]]

$\\cot \\alpha =$[[2]]

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Gegeven is de hoek $\\alpha$ in het eerste kwadrant en $\\cos \\alpha = \\frac{\\var{2*a+1}}{\\var{3a+2}}$. Bereken de andere goniometrische getallen van $\\alpha$.

", "advice": "

$\\sin \\alpha =$[[0]]

$\\tan \\alpha =$[[1]]

$\\cot \\alpha =$[[2]]

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