// Numbas version: exam_results_page_options
{"name": "Period amplitude phase shift (from eqn)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Period amplitude phase shift (from eqn)", "tags": [], "metadata": {"description": "<p>given trig equation. find period, amplitude and phase shift</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "", "advice": "<ul>\n<li>Amplitude: The number $\\var{a}$ next to the $cos$ tells you the amplitude. This is because it is the amount the original $y=cosx$ graph has been stretched in the y direction. You do not include the $\\var{e}$ in the amplitude as this only translates the graph in the y direction. It doesn't change the height of the graph from its middle point to its heighest or lowest value.</li>\n</ul>\n<p></p>\n<ul>\n<li>Period: The period of the function is the time for one wave. For the graph $y=cosx$ the period is $2 \\pi$. In the function above it has been stretched by a factor of $\\frac{\\var{c}}{\\var{b}}$ in the $x$ direction. This means that the period for function in the question is $2\\pi \\cdot \\frac{\\var{c}}{\\var{b}}$ which equals $\\var{period3sf}$</li>\n</ul>\n<p></p>\n<ul>\n<li>Phase shift: The phase shift is how far to the left or right the graph has moved from $y=cosx$. As the $x$ values have now been replaced by the values from $\\simplify{x+{d}}$ the graph moves to the $\\var{L_R}$ by $\\var{absd}$ units and so the phase shift is $\\simplify{0-{d}}$.</li>\n</ul>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1.1 .. 3#0.1)", "description": "<p>amplitude</p>", "templateType": "randrange", "can_override": false}, "e": {"name": "e", "group": "Ungrouped variables", "definition": "random(1 .. 12#1)", "description": "<p>vertical translation</p>", "templateType": "randrange", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(-3..3 except 0)", "description": "<p>negative of the phase shift</p>", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(3,5,7,11)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(2,4,8,13)", "description": "", "templateType": "anything", "can_override": false}, "absd": {"name": "absd", "group": "Ungrouped variables", "definition": "abs(d)", "description": "", "templateType": "anything", "can_override": false}, "left": {"name": "left", "group": "Ungrouped variables", "definition": "\"left\"", "description": "", "templateType": "string", "can_override": false}, "right": {"name": "right", "group": "Ungrouped variables", "definition": "\"right\"", "description": "", "templateType": "string", "can_override": false}, "L_R": {"name": "L_R", "group": "Ungrouped variables", "definition": "if(d>0,left,right)", "description": "", "templateType": "anything", "can_override": false}, "period": {"name": "period", "group": "Ungrouped variables", "definition": "2pi*(c)/(b)", "description": "", "templateType": "anything", "can_override": false}, "period3sf": {"name": "period3sf", "group": "Ungrouped variables", "definition": "sigformat(period,3)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "d", "absd", "e", "left", "right", "L_R", "period", "period3sf"], "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>What are the amplitude, period and phase shift (from $y=cosx^c$) for the following equation</p>\n<p></p>\n<p>\\[ y=\\var{a}cos \\left (\\frac{\\var{b}}{\\var{c}} (\\simplify{x^c+{d}}) \\right)+\\var{e} \\]</p>\n<p></p>\n<p>amplitude&nbsp; [[0]]</p>\n<p>period&nbsp; [[2]]$^c$&nbsp; &nbsp;Give your answer to 3 significant figures</p>\n<p>phase shift&nbsp; [[1]]$^c$&nbsp; &nbsp;Give your answer to 1 decimal place</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "amplitude", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{a}", "maxValue": "{a}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "1", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "phase shift", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "-{d}", "maxValue": "-{d}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "1", "precisionPartialCredit": 0, "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": "period", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "2pi*{c}/{b}", "maxValue": "2pi*{c}/{b}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": 0, "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/"}]}