// Numbas version: exam_results_page_options
{"name": "Trig Equation Basics (tan)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Trig Equation Basics (tan)", "tags": [], "metadata": {"description": "<p>Solving tanx in given interval. With random variation and worked solutions.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>Simpler Trig Questions</p>", "advice": "<p><span style=\"text-decoration: underline;\"><em><strong>WORKED SOLUTIONS</strong></em></span></p>\n<p>\\begin{align}<br/>tan(x)&amp;=\\var{t} \\\\\\\\<br/>x_1&amp;=tan^{-1}\\var{t}=\\var{t_1_3sf}^c \\\\\\\\<br/>x_2&amp;=\\var{t_1_5sf}+\\pi=\\var{t_2_3sf}^c<br/>\\end{align}</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"coeffsin": {"name": "coeffsin", "group": "Part 1 sin", "definition": "random(5 .. 10#1)", "description": "", "templateType": "randrange", "can_override": false}, "RHS": {"name": "RHS", "group": "Part 1 sin", "definition": "random(0 .. 4#1)", "description": "", "templateType": "randrange", "can_override": false}, "val_sin": {"name": "val_sin", "group": "Part 1 sin", "definition": "RHS/coeffsin", "description": "", "templateType": "anything", "can_override": false}, "first_soln": {"name": "first_soln", "group": "Part 1 sin", "definition": "arcsin({val_sin})*180/pi", "description": "", "templateType": "anything", "can_override": false}, "second_soln": {"name": "second_soln", "group": "Part 1 sin", "definition": "180-first_soln", "description": "", "templateType": "anything", "can_override": false}, "first_soln_3": {"name": "first_soln_3", "group": "Part 1 sin", "definition": "sigformat(first_soln,3)", "description": "", "templateType": "anything", "can_override": false}, "second_soln_3": {"name": "second_soln_3", "group": "Part 1 sin", "definition": "sigformat(second_soln,3)", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Part 2 cos", "definition": "random(16 .. 25#1)", "description": "", "templateType": "randrange", "can_override": false}, "b": {"name": "b", "group": "Part 2 cos", "definition": "random(-5 .. 5#1)", "description": "", "templateType": "randrange", "can_override": false}, "c": {"name": "c", "group": "Part 2 cos", "definition": "random(1 .. 10#1)", "description": "", "templateType": "randrange", "can_override": false}, "cosx": {"name": "cosx", "group": "Part 2 cos", "definition": "(c-b)/a", "description": "", "templateType": "anything", "can_override": false}, "x_1_3sf": {"name": "x_1_3sf", "group": "Part 2 cos", "definition": "sigformat(arccos({cosx}),3)", "description": "", "templateType": "anything", "can_override": false}, "x_2_3sf": {"name": "x_2_3sf", "group": "Part 2 cos", "definition": "sigformat(2pi-arccos({cosx}),3)", "description": "", "templateType": "anything", "can_override": false}, "x_3_3sf": {"name": "x_3_3sf", "group": "Part 2 cos", "definition": "sigformat(2pi+arccos({cosx}),3)", "description": "", "templateType": "anything", "can_override": false}, "x_1": {"name": "x_1", "group": "Part 2 cos", "definition": "arccos({cosx})", "description": "", "templateType": "anything", "can_override": false}, "x_2": {"name": "x_2", "group": "Part 2 cos", "definition": "2pi-arccos({cosx})", "description": "", "templateType": "anything", "can_override": false}, "x_3": {"name": "x_3", "group": "Part 2 cos", "definition": "2pi+arccos({cosx})", "description": "", "templateType": "anything", "can_override": false}, "x_1_6sf": {"name": "x_1_6sf", "group": "Part 2 cos", "definition": "sigformat(arccos({cosx}),6)", "description": "", "templateType": "anything", "can_override": false}, "first_soln_5": {"name": "first_soln_5", "group": "Part 1 sin", "definition": "sigformat(first_soln,5)", "description": "", "templateType": "anything", "can_override": false}, "t": {"name": "t", "group": "part c tan", "definition": "random(-3 .. 3#0.1)", "description": "", "templateType": "randrange", "can_override": false}, "t_1": {"name": "t_1", "group": "part c tan", "definition": "arctan({t})", "description": "", "templateType": "anything", "can_override": false}, "t_2": {"name": "t_2", "group": "part c tan", "definition": "{t_1}+pi", "description": "", "templateType": "anything", "can_override": false}, "t_1_5sf": {"name": "t_1_5sf", "group": "part c tan", "definition": "sigformat({t_1,5)", "description": "", "templateType": "anything", "can_override": false}, "t_1_3sf": {"name": "t_1_3sf", "group": "part c tan", "definition": "sigformat({t_1},3)", "description": "", "templateType": "anything", "can_override": false}, "t_2_3sf": {"name": "t_2_3sf", "group": "part c tan", "definition": "sigformat({t_2},3)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "Part 1 sin", "variables": ["coeffsin", "RHS", "val_sin", "second_soln", "first_soln", "first_soln_3", "second_soln_3", "first_soln_5"]}, {"name": "Part 2 cos", "variables": ["a", "b", "c", "cosx", "x_1_3sf", "x_2_3sf", "x_3_3sf", "x_1", "x_2", "x_3", "x_1_6sf"]}, {"name": "part c tan", "variables": ["t", "t_1", "t_2", "t_1_5sf", "t_1_3sf", "t_2_3sf"]}], "functions": {}, "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": "<p>Solve $tan(x)=\\var{t}$ between $-\\frac{\\pi}{2}\\leq x \\leq \\frac{3\\pi}{2}$</p>\n<p></p>\n<p>Write your answers below in <strong>ascending</strong> order and to 3 significant figures.</p>\n<p></p>\n<p>$x=$[[0]]$^c$ or [[1]]$^c$</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "t1", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{t_1}", "maxValue": "{t_1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "t2", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{t_2}", "maxValue": "{t_2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Mike Phipps", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/14139/"}]}]}], "contributors": [{"name": "Mike Phipps", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/14139/"}]}