// Numbas version: finer_feedback_settings {"name": "Musa's copy of 3 Geometry: trig on unit circle, short", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [["question-resources/Unit_circle.png", "/srv/numbas/media/question-resources/Unit_circle.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Musa's copy of 3 Geometry: trig on unit circle, short", "tags": [], "metadata": {"description": "

$x$ is given and (sin(x),cos(x)) is plotted on a unit circle.  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.) Also find values and sign of cos/tan/sin(x).

", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "extensions": ["jsxgraph"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"angle": {"name": "angle", "group": "Ungrouped variables", "definition": "[a]+shuffle([-a,180+a])+shuffle([360-a,180-a,90-a])", "description": "

The slope of the line.

", "templateType": "anything", "can_override": false}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "[cos(angle[0]/180*pi),\ncos(angle[1]/180*pi),\ncos(angle[3]/180*pi)]", "description": "

The y-intercept.

", "templateType": "anything", "can_override": false}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "[sin(angle[0]/180*pi),\nsin(angle[1]/180*pi),\nsin(angle[3]/180*pi)]", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random([13,14,15,16,17,-4,-5,-6,22,24,25])*10+random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "An": {"name": "An", "group": "Ungrouped variables", "definition": "random(0,30,45,60,90)", "description": "", "templateType": "anything", "can_override": false}, "index": {"name": "index", "group": "Ungrouped variables", "definition": "random(0..8)", "description": "", "templateType": "anything", "can_override": false}, "teta": {"name": "teta", "group": "Ungrouped variables", "definition": "[0,30,45,60,90,120,135,150,180]", "description": "", "templateType": "anything", "can_override": false}, "x_v": {"name": "x_v", "group": "Ungrouped variables", "definition": "[1,0.87,0.71,0.5,0,-0.50,-0.71,-0.87,-1]", "description": "", "templateType": "anything", "can_override": false}, "y_v": {"name": "y_v", "group": "Ungrouped variables", "definition": "[0,0.5,0.71,0.87,1,0.87,0.71,0.50,0]", "description": "", "templateType": "anything", "can_override": false}, "q": {"name": "q", "group": "Ungrouped variables", "definition": "random(0,3)", "description": "", "templateType": "anything", "can_override": false}, "tsct": {"name": "tsct", "group": "Ungrouped variables", "definition": "[[1,\"+\",\"+\",\"+\"],[2,\"+\",\"-\",\"-\"],[3,\"-\",\"-\",\"+\"],[4,\"-\",\"+\",\"-\"]]", "description": "", "templateType": "anything", "can_override": false}, "x_a": {"name": "x_a", "group": "Ungrouped variables", "definition": "random(1..359)", "description": "", "templateType": "anything", "can_override": false}, "sx_a": {"name": "sx_a", "group": "Ungrouped variables", "definition": "sin(x_a*pi/180)", "description": "", "templateType": "anything", "can_override": false}, "cx_a": {"name": "cx_a", "group": "Ungrouped variables", "definition": "cos(x_a*pi/180)", "description": "", "templateType": "anything", "can_override": false}, "tx_a": {"name": "tx_a", "group": "Ungrouped variables", "definition": "tan(x_a*pi/180)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "angle", "x", "y", "An", "index", "teta", "x_v", "y_v", "q", "tsct", "x_a", "sx_a", "cx_a", "tx_a"], "variable_groups": [], "functions": {"dragpointa": {"parameters": [["x0", "number"], ["y0", "number"]], "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\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": ""}, "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": "

{dragpointa(x[0],y[0])}

\n

\n

Use the diagram above to 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 $\\var{angle[0]}^{\\circ}$. If you hover the mouse over the point $A$, you will be shown its coordinates.

\n

Give your answer to 2 d.p..

\n

$\\sin(\\var{angle[0]}^{\\circ}) =$ [[0]]

\n

$\\cos(\\var{angle[0]}^{\\circ}) =$ [[1]]

\n

", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "precround(y[0],2)", "maxValue": "precround(y[0],2)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "precround(x[0],2)", "maxValue": "precround(x[0],2)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"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": "

\n

Find the point $(x,y)$ on the unit circle when A= {teta[index]}$^\\circ$

\n

(Give your answers to two decimal places):

\n

$x$ = [[0]] 

\n

$y$ = [[1]]

", "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": "{x_v[index]}", "maxValue": "{x_v[index]}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "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": "{y_v[index]}", "maxValue": "{y_v[index]}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}, {"name": "Musa Mammadov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4417/"}]}]}], "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}, {"name": "Musa Mammadov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4417/"}]}