// Numbas version: exam_results_page_options {"name": "Algebra. Trigonometric identities. II", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variables": {"marks": {"description": "", "templateType": "anything", "definition": "matrix(map(if(rand[j]=1,[max_mark/n,-max_mark/3+max_mark/n],[-max_mark/3+max_mark/n,max_mark/n]),j,0..n-1))\n", "name": "marks", "group": "do not change these"}, "rand": {"description": "", "templateType": "anything", "definition": "repeat(if(random(0..2)=2,1,0),n)", "name": "rand", "group": "do not change these"}, "n": {"description": "", "templateType": "anything", "definition": "14", "name": "n", "group": "change these"}, "max_mark": {"description": "", "templateType": "anything", "definition": "6", "name": "max_mark", "group": "change these"}, "statements_false": {"description": "", "templateType": "anything", "definition": "[ \"The formula $\\\\sin(A-B) = \\\\sin(A)\\\\cos(B) - \\\\cos(A)\\\\sin(B)$ is 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 \"There are exactly two formulas for $\\\\cos(2A)$ 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 \"$\\\\sin(20+5) = \\\\sin(20)\\\\cos(5) + \\\\cos(5)\\\\sin(20)$\",\n \"$\\\\sec^2(x) + 1 = \\\\tan^2(x)$\",\n \"$\\\\cot^2(x) + 1 = \\\\csc^2(t)$\",\n \"$\\\\cos(A+B)= \\\\cos(A)\\\\cos(B) + \\\\sin(A)\\\\sin(B)$ \" \n]", "name": "statements_false", "group": "change these"}, "statements": {"description": "", "templateType": "anything", "definition": "map(if(rand[j]=1,\n statements_true[j],\n statements_false[j]),j,0..n-1)", "name": "statements", "group": "do not change these"}, "statements_true": {"description": "", "templateType": "anything", "definition": "[ \"The formula $\\\\sin(A-B) = \\\\sin(A)\\\\cos(B) - \\\\cos(A)\\\\sin(B)$ is not 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 \"There are exactly three formulas for $\\\\cos(2A)$ 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 \"$\\\\sin(25) = \\\\sin(20)\\\\cos(5) + \\\\sin(5)\\\\cos(20)$\",\n \"$\\\\tan^2(x) + 1 = \\\\sec^2(x)$\",\n \"$\\\\csc^2(x)=\\\\cot^2(x) + 1$\",\n \"$\\\\cos(A+B)= \\\\cos(A)\\\\cos(B) - \\\\sin(A)\\\\sin(B)$ \" \n]\n ", "name": "statements_true", "group": "change these"}}, "metadata": {"description": "

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

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See 12.4, 12.5, 13.4 and the formula sheet.

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Which of the following are true and which are false? If you are unsure of something, find out the answer instead of guessing. A single error will result in a score 0 for the whole question. If you are unable to find out or understand the answer, you are welcome to ask me for help or advice.

\n

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The formula sheet is in Learning Materials folder in Blackboard.

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True

", "

False

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