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Notasjon: For å skrive inn rottegn, feks roten av 5, skriv sqrt(5)

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I denne oppgaven skal du tegne opp enhetssirkelen, repetere definisjonen på sinus og cosinus og regne ut verdiene for de oppgitte vinklene for hånd. Da trenger du litt kunnskap fra ungdomsskolen: pythagoras setning, egenskaper ved trekanter med vinklene 30, 60 og 90 og ved likebeinte trekanter.

\n

Fyll in tabellen med sinus- og cosinus verdiene til de oppgitte vinklene: 

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$v$$0^{\\circ}$$30^{\\circ}$$45^{\\circ}$$60^{\\circ}$$90^{\\circ}$$180^{\\circ}$$270^{\\circ}$$360^{\\circ}$
$\\sin(v)$[[0]][[1]][[2]][[3]][[4]][[5]][[6]][[7]]
$\\cos(v)$[[8]][[9]][[10]][[11]][[12]][[13]][[14]][[15]]
\n

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"implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "sqrt(3)/2", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], 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Bruk enhetssirkelen og skriv sinus og cosinus verdiene av disse vinklene i form av spisse vinkler

\n

{geogebra_applet('https://www.geogebra.org/m/gqba3v8x',defs2)}

\n

$\\sin(\\var{b}^{\\circ})=\\sin($[[0]]$^{\\circ})$

\n

$\\sin(\\var{b}^{\\circ})=\\cos($[[1]]$^{\\circ})$

\n

$\\cos(\\var{b}^{\\circ})=-\\cos($[[2]]$^{\\circ})$

\n

$\\cos(\\var{b}^{\\circ})=-\\sin($[[3]]$^{\\circ})$

", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "a", "maxValue": "a", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{90-a}", "maxValue": "{90-a}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "a", "maxValue": "a", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{90-a}", "maxValue": "{90-a}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Bruk enhetssirkelen og skriv sinus og cosinus verdiene av disse vinklene i form av spisse vinkler

\n

{geogebra_applet('https://www.geogebra.org/m/gqba3v8x',defs3)}

\n

$\\sin(\\var{c}^{\\circ})=-\\sin($[[0]]$^{\\circ})$

\n

$\\sin(\\var{c}^{\\circ})=-\\cos($[[1]]$^{\\circ})$

\n

$\\cos(\\var{c}^{\\circ})=-\\cos($[[2]]$^{\\circ})$

\n

$\\cos(\\var{c}^{\\circ})=-\\sin($[[3]]$^{\\circ})$

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Bruk enhetssirkelen og skriv sinus og cosinus verdiene av disse vinklene i form av spisse vinkler

\n

{geogebra_applet('https://www.geogebra.org/m/gqba3v8x',defs4)}

\n

$\\sin(\\var{d}^{\\circ})=-\\sin($[[0]]$^{\\circ})$

\n

$\\sin(\\var{d}^{\\circ})=-\\cos($[[1]]$^{\\circ})$

\n

$\\cos(\\var{d}^{\\circ})=\\cos($[[2]]$^{\\circ})$

\n

$\\cos(\\var{d}^{\\circ})=\\sin($[[3]]$^{\\circ})$

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