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{"name": "Geometry: trig on unit circle, short", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"extensions": ["jsxgraph"], "tags": [], "variables": {"angle": {"templateType": "anything", "group": "Ungrouped variables", "name": "angle", "definition": "[a]+shuffle([-a,180+a])+shuffle([360-a,180-a,90-a])", "description": "<p>The slope of the line.</p>"}, "x": {"templateType": "anything", "group": "Ungrouped variables", "name": "x", "definition": "[cos(angle[0]/180*pi),\ncos(angle[1]/180*pi),\ncos(angle[3]/180*pi)]", "description": "<p>The y-intercept.</p>"}, "y": {"templateType": "anything", "group": "Ungrouped variables", "name": "y", "definition": "[sin(angle[0]/180*pi),\nsin(angle[1]/180*pi),\nsin(angle[3]/180*pi)]", "description": ""}, "a": {"templateType": "anything", "group": "Ungrouped variables", "name": "a", "definition": "random([13,14,15,16,17,-4,-5,-6,22,24,25])*10+random(1..9)", "description": ""}}, "variablesTest": {"maxRuns": 100, "condition": ""}, "functions": {"dragpointa": {"type": "html", "parameters": [["x0", "number"], ["y0", "number"]], "language": "javascript", "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});\na.setProperty({fixed:true});\n\n//var b = board.create('point',[-0.2,0],{size:3});\n//var c = board.create('point',[0.2,0],{size:3});\n//var d = board.create('point',[0.4,0],{size:3});\n\n//b.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(y0);\n//  Numbas.exam.currentQuestion.parts[0].gaps[3].display.studentAnswer(x0);\n//});\n//c.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[6].display.studentAnswer(y0);\n//  Numbas.exam.currentQuestion.parts[0].gaps[7].display.studentAnswer(x0);\n//});\n//d.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(y0);\n//  Numbas.exam.currentQuestion.parts[0].gaps[7].display.studentAnswer(x0);\n//});\n\nreturn div;\n\n\n"}}, "preamble": {"js": "", "css": ""}, "ungrouped_variables": ["a", "angle", "x", "y"], "metadata": {"description": "<p>$x$ is given and (sin(x),cos(x)) is plotted on a unit circle.&nbsp; Then the student is asked to determine sin(y) and cos(y), where y is closely related to x (e.g. y=-x, y=180+x, etc.)</p>", "licence": "Creative Commons Attribution 4.0 International"}, "parts": [{"extendBaseMarkingAlgorithm": true, "type": "gapfill", "variableReplacements": [], "customName": "", "useCustomName": false, "unitTests": [], "gaps": [{"extendBaseMarkingAlgorithm": true, "type": "numberentry", "useCustomName": false, "correctAnswerFraction": false, "allowFractions": false, "unitTests": [], "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "mustBeReducedPC": 0, "customName": "", "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "showFractionHint": true, "maxValue": "precround(y[0],2)", "variableReplacements": [], "minValue": "precround(y[0],2)", "showCorrectAnswer": true, "showFeedbackIcon": true, "mustBeReduced": false, "marks": "0.5", "customMarkingAlgorithm": ""}, {"extendBaseMarkingAlgorithm": true, "type": "numberentry", "useCustomName": false, "correctAnswerFraction": false, "allowFractions": false, "unitTests": [], "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "mustBeReducedPC": 0, "customName": "", "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "showFractionHint": true, "maxValue": "precround(x[0],2)", "variableReplacements": [], "minValue": "precround(x[0],2)", "showCorrectAnswer": true, "showFeedbackIcon": true, "mustBeReduced": false, "marks": "0.5", "customMarkingAlgorithm": ""}], "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "adaptiveMarkingPenalty": 0, "scripts": {}, "marks": 0, "showCorrectAnswer": true, "sortAnswers": false, "prompt": "<p>{dragpointa(x[0],y[0])}</p>\n<p></p>\n<p>Use the diagram above to&nbsp;determine $\\sin(\\var{angle[0]}^{\\circ})$ and $\\cos(\\var{angle[0]}^{\\circ})$. To get to point $A$, we started at $(1,0)$ and rotated by $\\var{angle[0]}^{\\circ}$.&nbsp;If you hover the mouse over the point $A$, you will be shown its coordinates.</p>\n<p>Give your answer to 2 d.p..</p>\n<p>$\\sin(\\var{angle[0]}^{\\circ}) =$ [[0]]</p>\n<p>$\\cos(\\var{angle[0]}^{\\circ}) =$ [[1]]</p>\n<p></p>"}], "statement": "<p>This is a non-calculator question.</p>\n<p>-----------------------------------</p>", "rulesets": {}, "advice": "<p>See 7.3 and 7.5 for background and examples</p>", "variable_groups": [], "name": "Geometry: trig on unit circle, short", "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}]}], "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}