This uses an embedded Geogebra graph of a sine curve $y=a\\sin (bx+c)+d$ with random coefficients set by NUMBAS.
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "The graph shows a sine curve.
\n{geogebra_applet('https://ggbm.at/GqxVC76x', defs, [])}
\n", "advice": "", "rulesets": {}, "extensions": ["geogebra"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"b": {"name": "b", "group": "Ungrouped variables", "definition": "random(2,3,1/2)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "0", "description": "", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(-3..3 except 0)", "description": "", "templateType": "anything", "can_override": false}, "defs": {"name": "defs", "group": "Ungrouped variables", "definition": "[\n ['a',a],\n ['b',b],\n ['c',c],\n ['d',d],\n ['f',f]\n]", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(2..4)", "description": "", "templateType": "anything", "can_override": false}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "'{a}cos(({b}x)*pi/180)+{d}'", "description": "", "templateType": "anything", "can_override": false}, "fx": {"name": "fx", "group": "Ungrouped variables", "definition": "expression('{a}cos(({b}x))+{d}')", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "abs(a)+abs(d)<5", "maxRuns": "200"}, "ungrouped_variables": ["a", "b", "defs", "c", "d", "f", "fx"], "variable_groups": [], "functions": {"graph": {"parameters": [], "type": "html", "language": "jme", "definition": "geogebra_applet('https://ggbm.at/aXxv2ECN', defs, [])"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "What is the equation of this curve?
", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": "1", "showCellAnswerState": true, "choices": ["$y=\\simplify[unitFactor,fractionNumbers]{{a} sin({b}x+{c})+{d}}$
", "$y=\\simplify[unitFactor,fractionNumbers]{{a} sin({1/b}x+{c})+{d}}$
", "$y=\\simplify[unitFactor,fractionNumbers]{-{a} sin({b}x+{c})+{d}}$
", "$y=\\simplify[unitFactor,fractionNumbers]{{2a} sin({b}x-{c})+{d}}$
", "$y=\\simplify[unitFactor,fractionNumbers]{{a+1} sin({b}x-{c})+{2*d}}$
", "$y=\\simplify[unitFactor,fractionNumbers]{{a} sin({2*b}x+{c})+{d}}$
"], "matrix": ["2", 0, 0, 0, 0, 0], "distractors": ["", "", "", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}]}]}], "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}]}