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{"name": "Paul's copy of Geometry: trig on unit circle I", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"statement": "<p>This is a non-calculator question.</p>", "rulesets": {}, "variables": {"x": {"description": "<p>The y-intercept.</p>", "definition": "[cos(angle[0]/180*pi),\ncos(angle[1]/180*pi),\ncos(angle[2]/180*pi),\ncos(angle[3]/180*pi)]", "name": "x", "group": "Ungrouped variables", "templateType": "anything"}, "angle": {"description": "<p>The slope of the line.</p>", "definition": "shuffle([0,45,90,180,-45,-90])", "name": "angle", "group": "Ungrouped variables", "templateType": "anything"}, "y": {"description": "", "definition": "[sin(angle[0]/180*pi),\nsin(angle[1]/180*pi),\nsin(angle[2]/180*pi),\nsin(angle[3]/180*pi)]", "name": "y", "group": "Ungrouped variables", "templateType": "anything"}}, "tags": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Student is asked to drag points onto the unit circle, to represent sin(x) and cos(x), where x is a multiple of 45 degrees.</p>"}, "parts": [{"showFeedbackIcon": true, "marks": 0, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "unitTests": [], "extendBaseMarkingAlgorithm": true, "gaps": [{"maxValue": "x[0]+0.03", "unitTests": [], "minValue": "x[0]-0.03", "marks": "0.5", "allowFractions": false, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "correctAnswerFraction": false, "mustBeReduced": false, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "mustBeReducedPC": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "type": "numberentry", "scripts": {}, "customMarkingAlgorithm": "", "notationStyles": ["plain", "en", "si-en"]}, {"maxValue": "y[0]+0.03", "unitTests": [], "minValue": "y[0]-0.03", "marks": "0.5", "allowFractions": false, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "correctAnswerFraction": false, "mustBeReduced": false, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "mustBeReducedPC": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "type": "numberentry", "scripts": {}, "customMarkingAlgorithm": "", "notationStyles": ["plain", "en", "si-en"]}, {"maxValue": "x[1]+0.03", "unitTests": [], "minValue": "x[1]-0.03", "marks": "0.5", "allowFractions": false, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "correctAnswerFraction": false, "mustBeReduced": false, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "mustBeReducedPC": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "type": "numberentry", "scripts": {}, "customMarkingAlgorithm": "", "notationStyles": ["plain", "en", "si-en"]}, {"maxValue": "y[1]+0.03", "unitTests": [], "minValue": "y[1]-0.03", "marks": "0.5", "allowFractions": false, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "correctAnswerFraction": false, "mustBeReduced": false, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "mustBeReducedPC": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "type": "numberentry", "scripts": {}, "customMarkingAlgorithm": "", "notationStyles": ["plain", "en", "si-en"]}, {"maxValue": "x[2]+0.03", "unitTests": [], "minValue": "x[2]-0.03", "marks": "0.5", "allowFractions": false, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "correctAnswerFraction": false, "mustBeReduced": false, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "mustBeReducedPC": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "type": "numberentry", "scripts": {}, "customMarkingAlgorithm": "", "notationStyles": ["plain", "en", "si-en"]}, {"maxValue": "y[2]+0.03", "unitTests": [], "minValue": "y[2]-0.03", "marks": "0.5", "allowFractions": false, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "correctAnswerFraction": false, "mustBeReduced": false, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "mustBeReducedPC": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "type": "numberentry", "scripts": {}, "customMarkingAlgorithm": "", "notationStyles": ["plain", "en", "si-en"]}, {"maxValue": "x[3]+0.03", "unitTests": [], "minValue": "x[3]-0.03", "marks": "0.5", "allowFractions": false, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "correctAnswerFraction": false, "mustBeReduced": false, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "mustBeReducedPC": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "type": "numberentry", "scripts": {}, "customMarkingAlgorithm": "", "notationStyles": ["plain", "en", "si-en"]}, {"maxValue": "y[3]+0.03", "unitTests": [], "minValue": "y[3]-0.03", "marks": "0.5", "allowFractions": false, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "correctAnswerFraction": false, "mustBeReduced": false, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "mustBeReducedPC": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "type": "numberentry", "scripts": {}, "customMarkingAlgorithm": "", "notationStyles": ["plain", "en", "si-en"]}], "variableReplacements": [], "type": "gapfill", "prompt": "<p>{dragpoint()}</p>\n<p></p>\n<p>To&nbsp;determine $\\sin(\\var{angle[0]}^{\\text{o}})$ and $\\cos(\\var{angle[0]}^{\\text{o}})$ using the circle, where should we be? Move point $A$ to the appropriate location on the circle.</p>\n<p></p>\n<p>Then move $B$ to determine&nbsp;$\\sin(\\var{angle[1]+360}^{\\text{o}})$ and $\\cos(\\var{angle[1]+360}^{\\text{o}})$.</p>\n<p>Move $C$ to determine&nbsp;$\\sin(\\var{angle[2]-360}^{\\text{o}})$ and $\\cos(\\var{angle[2]-360}^{\\text{o}})$.</p>\n<p>Move $D$ to determine&nbsp;$\\simplify[fractionNumbers]{sin({angle[3]/180} * pi)}$ and $\\simplify[fractionNumbers]{cos({angle[3]/180} * pi)}$.</p>\n<p><span id=\"distance\"></span></p>", "scripts": {}, "customMarkingAlgorithm": "", "sortAnswers": false}], "variablesTest": {"maxRuns": 100, "condition": ""}, "name": "Paul's copy of Geometry: trig on unit circle I", "functions": {"dragpoint": {"type": "html", "definition": "// set up the board\nvar div = Numbas.extensions.jsxgraph.makeBoard('500px','500px',{boundingBox:[-1.2,1.2,1.2,-1.2],grid:true,labels:true});\nvar board = div.board;\n\n\n//plot circle of radius 1 centred at origin\nboard.create('functiongraph',\n         [function(x){ return Math.sqrt(1-x*x)},-1,1]);\nboard.create('functiongraph',\n         [function(x){ return -1*Math.sqrt(1-x*x)},-1,1]);\n\n\n\nvar a = board.create('point',[-0.4,0],{size:3});\nvar b = board.create('point',[-0.2,0],{size:3});\nvar c = board.create('point',[0.2,0],{size:3});\nvar d = board.create('point',[0.4,0],{size:3});\n\na.on('drag',function(){\n  var x0 = Numbas.math.niceNumber(a.X());\n  var y0 = Numbas.math.niceNumber(a.Y());\n  Numbas.exam.currentQuestion.parts[0].gaps[0].display.studentAnswer(x0);\n  Numbas.exam.currentQuestion.parts[0].gaps[1].display.studentAnswer(y0);\n});\nb.on('drag',function(){\n  var x0 = Numbas.math.niceNumber(b.X());\n  var y0 = Numbas.math.niceNumber(b.Y());\n  Numbas.exam.currentQuestion.parts[0].gaps[2].display.studentAnswer(x0);\n  Numbas.exam.currentQuestion.parts[0].gaps[3].display.studentAnswer(y0);\n});\nc.on('drag',function(){\n  var x0 = Numbas.math.niceNumber(c.X());\n  var y0 = Numbas.math.niceNumber(c.Y());\n  Numbas.exam.currentQuestion.parts[0].gaps[4].display.studentAnswer(x0);\n  Numbas.exam.currentQuestion.parts[0].gaps[5].display.studentAnswer(y0);\n});\nd.on('drag',function(){\n  var x0 = Numbas.math.niceNumber(d.X());\n  var y0 = Numbas.math.niceNumber(d.Y());\n  Numbas.exam.currentQuestion.parts[0].gaps[6].display.studentAnswer(x0);\n  Numbas.exam.currentQuestion.parts[0].gaps[7].display.studentAnswer(y0);\n});\n\nreturn div;\n\n\n", "parameters": [], "language": "javascript"}, "answer": {"type": "html", "definition": "// set up the board\nvar div = Numbas.extensions.jsxgraph.makeBoard('500px','500px',{boundingBox:[-1.2,1.2,1.2,-1.2],grid:true,labels:true});\nvar board = div.board;\n\n\n//plot circle of radius 1 centred at origin\nboard.create('functiongraph',\n         [function(x){ return Math.sqrt(1-x*x)},-1,1]);\nboard.create('functiongraph',\n         [function(x){ return -1*Math.sqrt(1-x*x)},-1,1]);\n\n\n\nvar a = board.create('point',[x0,y0],{size:3});\nvar b = board.create('point',[x1,y1],{size:3});\nvar c = board.create('point',[x2,y2],{size:3});\nvar d = board.create('point',[x3,y3],{size:3});\n\n\n\nreturn div;\n\n", "parameters": [["x0", "number"], ["y0", "number"], ["x1", "number"], ["y1", "number"], ["x2", "number"], ["y2", "number"], ["x3", "number"], ["y3", "number"]], "language": "javascript"}}, "extensions": ["jsxgraph"], "preamble": {"js": "", "css": ""}, "advice": "<p>{answer(x[0],y[0],x[1],y[1],x[2],y[2],x[3],y[3])}</p>\n<p></p>\n<p>See Lecture 6.1.</p>", "ungrouped_variables": ["angle", "x", "y"], "variable_groups": [], "type": "question", "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}, {"name": "Paul Emanuel", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2551/"}]}]}], "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}, {"name": "Paul Emanuel", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2551/"}]}