// Numbas version: finer_feedback_settings
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"anything", "name": "angle", "definition": "[a]+shuffle([-a,180+a])+shuffle([360-a,180-a,90-a])", "description": "<p>The slope of the line.</p>", "group": "Ungrouped variables"}, "y": {"templateType": "anything", "name": "y", "definition": "[sin(angle[0]/180*pi),\nsin(angle[1]/180*pi),\nsin(angle[3]/180*pi)]", "description": "", "group": "Ungrouped variables"}, "a": {"templateType": "anything", "name": "a", "definition": "random(1..7 except 4)*10+random(1..9)", "description": "", "group": "Ungrouped variables"}}, "preamble": {"css": "", "js": ""}, "functions": {"dragpointa": {"type": "html", "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\nvar b = board.create('point',[-0.2,0],{size:3});\nvar c = board.create('point',[0.2,0],{size:3});\n//var d = board.create('point',[0.4,0],{size:3});\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(y0);\n  Numbas.exam.currentQuestion.parts[0].gaps[3].display.studentAnswer(x0);\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[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//  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"advice": "<p>{answera(x[0],y[0],x[1],y[1],x[2],y[2])}</p>\n<p></p>\n<p>See Lecture 6.1&nbsp;and Question 7 on Workshop 6.2</p>", "parts": [{"type": "gapfill", "sortAnswers": false, "unitTests": [], "scripts": {}, "showCorrectAnswer": true, "gaps": [{"type": "numberentry", "maxValue": "precround(y[0],2)", "notationStyles": ["plain", "en", "si-en"], "unitTests": [], "scripts": {}, "correctAnswerFraction": false, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "minValue": "precround(y[0],2)", "correctAnswerStyle": "plain", "showFeedbackIcon": true, "allowFractions": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "customMarkingAlgorithm": "", "mustBeReduced": false, "marks": "0.5", "mustBeReducedPC": 0}, {"type": "numberentry", "maxValue": "precround(x[0],2)", "notationStyles": ["plain", "en", "si-en"], "unitTests": [], "scripts": {}, "correctAnswerFraction": false, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "minValue": "precround(x[0],2)", "correctAnswerStyle": "plain", "showFeedbackIcon": true, "allowFractions": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "customMarkingAlgorithm": "", "mustBeReduced": false, "marks": "0.5", "mustBeReducedPC": 0}, {"type": "numberentry", "maxValue": "y[1]+0.05", "notationStyles": ["plain", "en", "si-en"], "unitTests": [], "scripts": {}, "correctAnswerFraction": false, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "minValue": "y[1]-0.05", "correctAnswerStyle": "plain", "showFeedbackIcon": true, "allowFractions": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "customMarkingAlgorithm": "", "mustBeReduced": false, "marks": "0.5", "mustBeReducedPC": 0}, {"type": "numberentry", "maxValue": "x[1]+0.05", "notationStyles": ["plain", "en", "si-en"], "unitTests": [], "scripts": {}, "correctAnswerFraction": false, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "minValue": "x[1]-0.05", "correctAnswerStyle": "plain", "showFeedbackIcon": true, "allowFractions": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "customMarkingAlgorithm": "", "mustBeReduced": false, "marks": "0.5", "mustBeReducedPC": 0}, {"type": "numberentry", "maxValue": "precround(y[1],2)", "notationStyles": ["plain", "en", "si-en"], "unitTests": [], "scripts": {}, "correctAnswerFraction": false, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "minValue": "precround(y[1],2)", "correctAnswerStyle": "plain", "showFeedbackIcon": true, "allowFractions": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "customMarkingAlgorithm": "", "mustBeReduced": false, "marks": "0.5", "mustBeReducedPC": 0}, {"type": "numberentry", "maxValue": "precround(x[1],2)", "notationStyles": ["plain", "en", "si-en"], "unitTests": [], "scripts": {}, "correctAnswerFraction": false, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "minValue": "precround(x[1],2)", "correctAnswerStyle": "plain", "showFeedbackIcon": true, "allowFractions": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "customMarkingAlgorithm": "", "mustBeReduced": false, "marks": "0.5", "mustBeReducedPC": 0}, {"type": "numberentry", "maxValue": "y[2]+0.05", "notationStyles": ["plain", "en", "si-en"], "unitTests": [], "scripts": {}, "correctAnswerFraction": false, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "minValue": "y[2]-0.05", "correctAnswerStyle": "plain", "showFeedbackIcon": true, "allowFractions": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "customMarkingAlgorithm": "", "mustBeReduced": false, "marks": "0.5", "mustBeReducedPC": 0}, {"type": "numberentry", "maxValue": "x[2]+0.05", "notationStyles": ["plain", "en", "si-en"], "unitTests": [], "scripts": {}, "correctAnswerFraction": false, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "minValue": "x[2]-0.05", "correctAnswerStyle": "plain", "showFeedbackIcon": true, "allowFractions": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "customMarkingAlgorithm": "", "mustBeReduced": false, "marks": "0.5", "mustBeReducedPC": 0}, {"type": "numberentry", "maxValue": "precround(y[2],2)", "notationStyles": ["plain", "en", "si-en"], "unitTests": [], "scripts": {}, "correctAnswerFraction": false, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "minValue": "precround(y[2],2)", "correctAnswerStyle": "plain", "showFeedbackIcon": true, "allowFractions": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "customMarkingAlgorithm": "", "mustBeReduced": false, "marks": "0.5", "mustBeReducedPC": 0}, {"type": "numberentry", "maxValue": "precround(x[2],2)", "notationStyles": ["plain", "en", "si-en"], "unitTests": [], "scripts": {}, "correctAnswerFraction": false, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "minValue": "precround(x[2],2)", "correctAnswerStyle": "plain", "showFeedbackIcon": true, "allowFractions": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "customMarkingAlgorithm": "", "mustBeReduced": false, "marks": "0.5", "mustBeReducedPC": 0}], "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "prompt": "<p>{dragpointa(x[0],y[0])}</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,&nbsp;point $A$ was drawn.</p>\n<p></p>\n<p>(i) Use this to determine the following to 2 d.p.. (If you hover the mouse over the point $A$, you will be shown its coordinates.)</p>\n<p>$\\sin(\\var{angle[0]}^{\\text{o}}) =$ [[0]]</p>\n<p>$\\cos(\\var{angle[0]}^{\\text{o}}) =$ [[1]]</p>\n<p></p>\n<p></p>\n<p>(ii) We want to determine&nbsp;$\\sin(\\var{angle[1]}^{\\text{o}})$ and $\\cos(\\var{angle[1]}^{\\text{o}})$.</p>\n<p>First move $B$ to the appropriate location on the circle.&nbsp; Hence, work out $\\sin$ and $\\cos$ to 2 d.p..</p>\n<p>$\\sin(\\var{angle[1]}^{\\text{o}}) =$ [[4]]</p>\n<p>$\\cos(\\var{angle[1]}^{\\text{o}}) =$ [[5]]</p>\n<p></p>\n<p>Hint: you first need to work out the connection between $\\var{angle[1]}$ and $\\var{angle[0]}$. Sometimes it is obvious (e.g. new angle is the negative of the original angle) but sometimes it is tricky (e.g. new angle is 180 minus the old angle).</p>\n<p></p>\n<p></p>\n<p></p>\n<p></p>\n<p>(iii) Do the same for&nbsp;$\\sin(\\var{angle[3]}^{\\text{o}})$ and $\\cos(\\var{angle[3]}^{\\text{o}})$ using $C$. First move $C$ then enter the numbers.</p>\n<p>$\\sin(\\var{angle[3]}^{\\text{o}}) =$ [[8]]</p>\n<p>$\\cos(\\var{angle[3]}^{\\text{o}}) =$ [[9]]</p>\n<p></p>\n<p><span id=\"distance\"></span></p>", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "customMarkingAlgorithm": "", "marks": 0}], "statement": "<p>This is a non-calculator question.</p>", "variablesTest": {"maxRuns": 100, "condition": ""}, "type": "question", "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}], "resources": []}]}], "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}