// Numbas version: exam_results_page_options
{"name": "Trig Equation 2 (translation)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Trig Equation 2 (translation)", "tags": [], "metadata": {"description": "<p>solve trig equation involving a translation in given internval. with worked solutions</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>Trig equation with a translation</p>", "advice": "<p>\\begin{align}<br/><br/>sin \\left(x-\\frac{\\pi}{2} \\right) &amp; =\\var{a} \\\\\\\\<br/>\\left(x-\\frac{\\pi}{2} \\right) &amp; = sin^{-1}(\\var{a})=\\var{x1n} \\\\\\\\<br/>\\text{for $sinx$ you can find a second solution by going $\\pi-x_1$} \\\\\\\\<br/>\\left(x-\\frac{\\pi}{2} \\right) &amp; = \\pi-\\var{x1n}=\\var{x2n} \\\\\\\\<br/><br/>\\end{align}</p>\n<p>As the range of solution goes down to $-2\\pi$ you can find two more angles by taking away $2\\pi$ from the first two angles.</p>\n<p>\\begin{align}<br/><br/>x_3 &amp;=\\var{x1n}-2\\pi=\\var{x3n} \\\\\\\\<br/>x_4 &amp;=\\var{x2n}-2\\pi=\\var{x4n}<br/><br/>\\end{align}</p>\n<p>In ascending order your three solutions so far are</p>\n<p>\\begin{align}<br/>\\left(x-\\frac{\\pi}{2} \\right) &amp; =\\var{x3n} \\text{&nbsp; &nbsp;or&nbsp; &nbsp;} \\var{x4n} \\text{&nbsp; &nbsp;or&nbsp; &nbsp;} \\var{x1n} \\text{&nbsp; &nbsp;or&nbsp; &nbsp;} \\var{x2n}<br/>\\end{align}</p>\n<p>To find $x$ all you need to do now is add $\\frac{\\pi}{2}$</p>\n<p>\\begin{align}<br/>x=\\var{x3} \\text{&nbsp; &nbsp;or&nbsp; &nbsp;} \\var{x4} \\text{&nbsp; &nbsp;or&nbsp; &nbsp;} \\var{x1} \\text{&nbsp; &nbsp;or&nbsp; &nbsp;} \\var{x2}<br/>\\end{align}</p>\n<p>To 3 significant figures this gives</p>\n<p>\\begin{align}<br/>x=\\var{x3_3}^c \\text{&nbsp; &nbsp;or&nbsp; &nbsp;} \\var{x4_3}^c \\text{&nbsp; &nbsp;or&nbsp; &nbsp;} \\var{x1_3}^c \\text{&nbsp; &nbsp;or&nbsp; &nbsp;} \\var{x2_3}^c<br/>\\end{align}</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-0.95 .. 0.95#0.05)", "description": "", "templateType": "randrange", "can_override": false}, "x1n": {"name": "x1n", "group": "Ungrouped variables", "definition": "arcsin(a)", "description": "", "templateType": "anything", "can_override": false}, "x2n": {"name": "x2n", "group": "Ungrouped variables", "definition": "pi-x1n", "description": "", "templateType": "anything", "can_override": false}, "x3n": {"name": "x3n", "group": "Ungrouped variables", "definition": "x1n-2pi", "description": "", "templateType": "anything", "can_override": false}, "x4n": {"name": "x4n", "group": "Ungrouped variables", "definition": "x2n-2pi", "description": "", "templateType": "anything", "can_override": false}, "x1": {"name": "x1", "group": "Ungrouped variables", "definition": "x1n+pi/2", "description": "", "templateType": "anything", "can_override": false}, "x2": {"name": "x2", "group": "Ungrouped variables", "definition": "x2n+pi/2", "description": "", "templateType": "anything", "can_override": false}, "x3": {"name": "x3", "group": "Ungrouped variables", "definition": "x3n+pi/2", "description": "", "templateType": "anything", "can_override": false}, "x4": {"name": "x4", "group": "Ungrouped variables", "definition": "x4n+pi/2", "description": "", "templateType": "anything", "can_override": false}, "x1_3": {"name": "x1_3", "group": "Ungrouped variables", "definition": "sigformat(x1,3)", "description": "", "templateType": "anything", "can_override": false}, "x2_3": {"name": "x2_3", "group": "Ungrouped variables", "definition": "sigformat(x2,3)", "description": "", "templateType": "anything", "can_override": false}, "x3_3": {"name": "x3_3", "group": "Ungrouped variables", "definition": "sigformat(x3,3)", "description": "", "templateType": "anything", "can_override": false}, "x4_3": {"name": "x4_3", "group": "Ungrouped variables", "definition": "sigformat(x4,3)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "x1n", "x2n", "x3n", "x4n", "x1", "x2", "x3", "x4", "x1_3", "x2_3", "x3_3", "x4_3"], "variable_groups": [], "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 $sin \\left(x-\\frac{\\pi}{2} \\right)=\\var{a}$ between 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