// Numbas version: exam_results_page_options {"name": " Finding multipe solutions of sin(x)= (in degrees -360 to 360) WORKING", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": " Finding multipe solutions of sin(x)= (in degrees -360 to 360) WORKING", "tags": [], "metadata": {"description": "

Given the original formula the student enters the transformed formula

\n

", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

{eqnline(a,b,x2,y2,v,sin0)}

\n

The graph  shows the functions, \$y=sin(x^{\\circ})\$  and \$y=\\var{sin0}\$

", "advice": "", "rulesets": {}, "extensions": ["jsxgraph"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-4..4 except 0)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "a*b", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-5..5 except [0,a,-a])", "description": "", "templateType": "anything", "can_override": false}, "random": {"name": "random", "group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "templateType": "anything", "can_override": false}, "sin0": {"name": "sin0", "group": "Ungrouped variables", "definition": "random/10", "description": "", "templateType": "anything", "can_override": false}, "v": {"name": "v", "group": "Ungrouped variables", "definition": "random(2..4)", "description": "", "templateType": "anything", "can_override": false}, "x2": {"name": "x2", "group": "Ungrouped variables", "definition": "random(-3..3 except -1..1)", "description": "", "templateType": "anything", "can_override": false}, "y2": {"name": "y2", "group": "Ungrouped variables", "definition": "x2*a+b", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "x2", "b", "y2", "c", "v", "sin0", "random"], "variable_groups": [], "functions": {"eqnline": {"parameters": [["a", "number"], ["b", "number"], ["x2", "number"], ["y2", "number"], ["v", "number"], ["sin0", "number"]], "type": "html", "language": "javascript", "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;"}}, "preamble": {"js": "", "css": ""}, "parts": [{"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": "

Calulate the solutions to the equation \$sin(x^{\\circ})=\\var{sin0}\$  in the range \$-360^{\\circ} \\leqslant x ^{\\circ}\\leqslant 360 ^{\\circ}\$

\n

Give your values of \$x\$ in assending order.

\n

The smallest value is \$x=\\;\$[[0]]

\n

The next largest value of \$x=\\;\$[[1]]

\n

The next largest value of \$x=\\;\$[[2]]

\n

The  largest value of \$x=\\;\$ [[3]]

\n

", "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": "(-(2*pi)+arcsin({sin0}))*180/pi", "maxValue": "(-(2*pi)+arcsin({sin0}))*180/pi", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "

", "strictPrecision": false, "showPrecisionHint": 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": "(-pi-arcsin({sin0}))*180/pi", "maxValue": "(-pi-arcsin({sin0}))*180/pi", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "

", "strictPrecision": false, "showPrecisionHint": 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": "(arcsin({sin0}))*180/pi", "maxValue": "(arcsin({sin0}))*180/pi", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "

", "strictPrecision": false, "showPrecisionHint": 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": "(pi-arcsin({sin0}))*180/pi", "maxValue": "(pi-arcsin({sin0}))*180/pi", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "