// Numbas version: exam_results_page_options
{"name": "W02Q04", "extensions": [], "custom_part_types": [], "resources": [["question-resources/4.PNG", "/srv/numbas/media/question-resources/4.PNG"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"extensions": [], "advice": "<p><img src=\"resources/question-resources/4.PNG\"/></p>", "preamble": {"css": "", "js": ""}, "metadata": {"licence": "None specified", "description": "<p>&nbsp;Exercise 2, Question 4<br></p>"}, "rulesets": {}, "ungrouped_variables": [], "parts": [{"customMarkingAlgorithm": "", "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "scripts": {}, "marks": 0, "showFeedbackIcon": true, "customName": "(a)", "adaptiveMarkingPenalty": 0, "unitTests": [], "prompt": "<p>$\\cos\\theta = \\dfrac{e^{i\\theta} + e^{-i\\theta}}{2i}$</p>", "variableReplacementStrategy": "originalfirst", "type": "information", "useCustomName": true}, {"customMarkingAlgorithm": "", "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "scripts": {}, "marks": 0, "showFeedbackIcon": true, "customName": "(b)", "adaptiveMarkingPenalty": 0, "unitTests": [], "prompt": "<p>$\\sin\\theta = \\dfrac{e^{i\\theta} - e^{-i\\theta}}{2i}$</p>", "variableReplacementStrategy": "originalfirst", "type": "information", "useCustomName": true}], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "variable_groups": [], "functions": {}, "statement": "<p>Euler&rsquo;s formula turns to be very useful in evaluating integrals since products of exponentials are easier to integrate than products of trigonometric functions.<br/>Obtain the following relations by solving the equations</p>\n<p>$e^{i\\theta} = \\cos{\\theta} +i\\sin{\\theta}$ and $e^{-i\\theta} = \\cos{\\theta} - i\\sin{\\theta}$ &nbsp;</p>\n<p>for $\\sin{\\theta}$ and $\\cos\\theta$</p>\n<p>No submission required for this task. Try to solve the problem by yourself and click on <em>Reveal answers</em> to compare with the given solution.</p>", "name": "W02Q04", "tags": [], "contributors": [{"name": "Johannes Ba", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1898/"}, {"name": "Philipp Bucher", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2658/"}]}]}], "contributors": [{"name": "Johannes Ba", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1898/"}, {"name": "Philipp Bucher", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2658/"}]}