// Numbas version: exam_results_page_options
{"name": "Finding multipe solutions of sin(x)= (in degrees) ", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {"eqnline": {"definition": "// This function creates the board and sets it up, then returns an\n// HTML div tag containing the board.\n\n//Put in your values of x here\n\nvar x_min = -380;\nvar x_max = 380;\nvar y_min = -1.5;\nvar y_max = 1.5;\n\n// First, make the JSXGraph board.\n// The function provided by the JSXGraph extension wraps the board up in \n// a div tag so that it's easier to embed in the page.\nvar div = Numbas.extensions.jsxgraph.makeBoard('600px','600px',\n//{boundingBox: [-8,10,8,-10],\n {boundingBox: [x_min,y_max,x_max,y_min],                                           \n axis: false,\n showNavigation: true,\n grid: true\n});\n\n\n\n\n// div.board is the object created by JSXGraph, which you use to \n// manipulate elements\nvar board = div.board; \n\n// create the x-axis.\nvar xaxis = board.create('axis',[[0,0],[1,0]], {strokeColor: 'black', fixed: true,\n  name:'x', \n\t\t\t\n  withLabel: true, \n\t\t\tlabel: {position: 'rt',  // possible values are 'lft', 'rt', 'top', 'bot'\n\t\t\t\t\t offset: [-15, 20]   // (in pixels)\n\t\t\t\t\t }\n\n});\nxaxis.removeAllTicks();\nvar xticks = board.create('ticks',[xaxis,60],{\n\n  drawLabels: true,\n  label: {offset: [-10, -20]},\n  minorTicks: 0\n});\n\n\n// create the line y= value  which is sin0.\n\n\nboard.create('line',[[x_min,sin0],[x_max,sin0]],{strokeColor:'red',\n                                                 //name:'y=sin0', \n                                                 name:sin0,\n\t\t\t\n  withLabel: true, \n\t\t\tlabel: {position: 'top',  // possible values are 'lft', 'rt', 'top', 'bot'\n\t\t\t\t\t offset: [-45, 10]   // (in pixels)\n\t\t\t\t\t }\n\n});\n\n// create the y-axis\n\nvar yaxis = board.create('axis',[[0,0],[0,1]], { strokeColor: 'black', fixed: true,\n name:'sin(x)', \n\t\t\t\n  withLabel: true, \n\t\t\tlabel: {position: 'top',  // possible values are 'lft', 'rt', 'top', 'bot'\n\t\t\t\t\t offset: [-45, 240]   // (in pixels)\n\t\t\t\t\t }\n\n});\n\n\nyaxis.removeAllTicks();\nvar yticks = board.create('ticks',[yaxis,1],{\ndrawLabels: true,\nlabel: {offset: [-20, 0]},\nminorTicks: 0\n});\n\n\n // PUT YOUR FUNCTION HERE\n\n// sin (x) in degrees\nboard.create('functiongraph',[function(x){ return Math.sin(x*(Math.PI/180));},x_min,x_max]);\n//board.create('functiongraph',[function(x){ return Math.sin(x*(Math.PI/180))+v;},-360,360],{ strokeColor: 'red'});\n//board.create('functiongraph',[function(x){ return Math.sin(x*(Math.PI/180))-(v+1);},-360,360],{ strokeColor: 'black'});\n//Change axis range from -360 tp +360  y from -8 to +8 \n\n//board.create('functiongraph',[function(x){ return Math.exp(x);},x_min,x_max]);\n//board.create('functiongraph',[function(x){ return Math.log(x);},x_min,x_max]);\n//board.create('functiongraph',[function(x){ return (x);},x_min,x_max]);\n\n\n//board.create('functiongraph',[function(x){ return (x-a)*(x-b);},-8,8]);\n//board.create('functiongraph',[function(x){ return (x-a)*(x-b)+v;},-8,8],{ strokeColor: 'red'});\n\n//board.create('functiongraph',[function(x){ return x*x;},-8,8]);\n//board.create('functiongraph',[function(x){ return x*x+v;},-8,8],{ strokeColor: 'red'});\n//board.create('functiongraph',[function(x){ return x*x-(v+1);},-8,8],{ strokeColor: 'black'});\n\n\n//board.create('functiongraph',[function(x){ return x*x;},-8,8]);\n//board.create('functiongraph',[function(x){ return (x-v)*(x-v);},-8,8],{ strokeColor: 'red'});\n//board.create('functiongraph',[function(x){ return (x+v+1)*(x+v+1);},-8,8],{ strokeColor: 'black'});\n\n//board.create('functiongraph',[function(x){ return x*x;},-8,8]);\n//board.create('functiongraph',[function(x){ return v*(x)*(x);},-8,8],{ strokeColor: 'red'});\n//board.create('functiongraph',[function(x){ return (1/v)*(x)*(x);},-8,8],{ strokeColor: 'black'});\n\n//board.create('functiongraph',[function(x){ return (x)*(x)+v;},-8,8]);\n//board.create('functiongraph',[function(x){ return -((x)*(x)+v);},-8,8],{ strokeColor: 'red'});\n//board.create('functiongraph',[function(x){ return -(x)*(x);},-8,8],{ strokeColor: 'black'});\n\n\n\n\n\n\nreturn div;", "type": "html", "language": "javascript", "parameters": [["a", "number"], ["b", "number"], ["x2", "number"], ["y2", "number"], ["v", "number"], ["sin0", "number"]]}}, "ungrouped_variables": ["a", "x2", "b", "y2", "c", "v", "sin0", "random"], "name": "Finding multipe solutions of sin(x)= (in degrees) ", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>Calulate the solutions to the equation $sin(x)=\\var{sin0}$ &nbsp;in the range $-360 \\leqslant x \\leqslant&nbsp;360$</p>\n<p>Give your values of $x$ in assending order.</p>\n<p>The smallest value is $x=\\;$[[0]]&nbsp; &nbsp;</p>\n<p>The next largest value of $x=\\;$[[1]]</p>\n<p>The next largest value of $x=\\;$[[2]]</p>\n<p>The largest value is $x=\\;$[[3]]</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(-2*pi+arcsin({sin0}))*180/pi", "strictPrecision": false, "minValue": "(-2*pi+arcsin({sin0}))*180/pi", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "showPrecisionHint": true, "type": "numberentry"}, {"precisionType": "dp", "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(-pi-arcsin({sin0}))*180/pi", "strictPrecision": false, "minValue": "(-pi-arcsin({sin0}))*180/pi", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "showPrecisionHint": true, "type": "numberentry"}, {"precisionType": "dp", "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "arcsin({sin0)*180/pi", "strictPrecision": false, "minValue": "arcsin({sin0)*180/pi", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "showPrecisionHint": true, "type": "numberentry"}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "(pi-arcsin({sin0}))*180/pi", "strictPrecision": true, "minValue": "(pi-arcsin({sin0}))*180/pi", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "showPrecisionHint": true, "type": "numberentry"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": ["jsxgraph"], "statement": "<p>{eqnline(a,b,x2,y2,v,sin0)}</p>\n<p>The graph &nbsp;shows the functions,&nbsp;$y=sin(x)$ &nbsp;and $y=\\var{sin0}$</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(-4..4 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "a*b", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(-5..5 except [0,a,-a])", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "random": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "random", "description": ""}, "sin0": {"definition": "random/10", "templateType": "anything", "group": "Ungrouped variables", "name": "sin0", "description": ""}, "v": {"definition": "random(2..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "v", "description": ""}, "x2": {"definition": "random(-3..3 except -1..1)", "templateType": "anything", "group": "Ungrouped variables", "name": "x2", "description": ""}, "y2": {"definition": "x2*a+b", "templateType": "anything", "group": "Ungrouped variables", "name": "y2", "description": ""}}, "metadata": {"description": "<p>Multiple solutions of sin(x) = .... &nbsp; $-360 \\leqslant x \\leqslant&nbsp;360$</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "steve kilgallon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/268/"}]}]}], "contributors": [{"name": "steve kilgallon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/268/"}]}