// Numbas version: exam_results_page_options {"name": "Algebra. Trigonometric identities. I", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Algebra. Trigonometric identities. I", "tags": [], "metadata": {"description": "

several statements are given regarding trig identities. student is to select which are true and which are false

See ?? and the formula sheet.

", "rulesets": {}, "extensions": [], "variables": {"statements_false": {"name": "statements_false", "group": "change these", "definition": "[\"The formula $\\\\tan(A) = \\\\frac{\\\\sin(A)}{\\\\cos(A)}$ is not in the formula sheet\",\n \"The formula $\\\\cos(A+2\\\\pi) = \\\\cos(A)$ is in the formula sheet\",\n \"The formula $\\\\cos(2A) = 1-2\\\\sin^2(A)$ is not in the formula sheet\",\n \"$\\\\cos^2(t) = \\\\frac{1}{2} \\\\cos(2t)- \\\\frac{1}{2}$\",\n \"$\\\\sin^2(z) = \\\\frac{1}{2} \\\\cos(2z) -\\\\frac{1}{2}$\",\n \"$\\\\sec(\\\\theta) = \\\\frac{1}{\\\\sin(\\\\theta)}$\",\n \"$\\\\csc(\\\\theta) = \\\\frac{1}{\\\\cos(\\\\theta)}$\",\n \"$\\\\cot(\\\\theta) = \\\\tan^{-1}(x)$\",\n \"$\\\\sin(-a) = \\\\sin\\\\times (-a)$\",\n \"$-\\\\cos(q) = \\\\cos(-q)$\"\n]", "description": "", "templateType": "anything"}, "statements_true": {"name": "statements_true", "group": "change these", "definition": "[\"The formula $\\\\tan(A) = \\\\frac{\\\\sin(A)}{\\\\cos(A)}$ is in the formula sheet\",\n \"The formula $\\\\cos(A+2\\\\pi) = \\\\cos(A)$ is not in the formula sheet\",\n \"The formula $\\\\cos(2A) = 1-2\\\\sin^2(A)$ is in the formula sheet\",\n \"$\\\\cos^2(t) = \\\\frac{1}{2} \\\\cos(2t)+ \\\\frac{1}{2}$\",\n \"$\\\\sin^2(z) = \\\\frac{1}{2} - \\\\frac{1}{2} \\\\cos(2z)$\",\n \"$\\\\sec(\\\\theta) = \\\\frac{1}{\\\\cos(\\\\theta)}$\",\n \"$\\\\csc(\\\\theta) = \\\\frac{1}{\\\\sin(\\\\theta)}$\",\n \"$\\\\cot(\\\\theta) = \\\\frac{1}{\\\\tan(\\\\theta)}$\",\n \"$\\\\sin(-a) = -\\\\sin(a)$\",\n \"$\\\\cos(q) = \\\\cos(-q)$\"\n]\n ", "description": "", "templateType": "anything"}, "error": {"name": "error", "group": "change these", "definition": "1/4", "description": "", "templateType": "anything"}, "marks": {"name": "marks", "group": "do not change these", "definition": "matrix(map(if(rand[j]=1,[max_mark/n,-max_mark*error+max_mark/n],[-max_mark*error+max_mark/n,max_mark/n]),j,0..n-1))", "description": "", "templateType": "anything"}, "n": {"name": "n", "group": "change these", "definition": "len(statements_true)", "description": "", "templateType": "anything"}, "max_mark": {"name": "max_mark", "group": "change these", "definition": "4", "description": "", "templateType": "anything"}, "rand": {"name": "rand", "group": "do not change these", "definition": "repeat(if(random(0..3)=3,1,0),n)", "description": "", "templateType": "anything"}, "statements": {"name": "statements", "group": "do not change these", "definition": "map(if(rand[j]=1,\n statements_true[j],\n statements_false[j]),j,0..n-1)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "change these", "variables": ["statements_true", "statements_false", "max_mark", "n", "error"]}, {"name": "do not change these", "variables": ["rand", "statements", "marks"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_x", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "
\n
• Which of the following are true and which are false? If you are unsure of something, find out the answer instead of guessing.
• \n
• Each error will cost 1 of the available marks.
• \n
• The formula sheet is at the end of the module handbook. A digital copy of the handbook is available on Blackboard.
• \n