\$\\var{a}\\sin(x)=\\var{a-1}\$

\n
\n
• $\\sin(x)=$ [[0]]
• \n
• $x=$ [[1]]$^\\circ$, [[2]]$^\\circ$, [[3]]$^\\circ$ or [[4]]$^\\circ$
• \n

\$\\var{b}\\cos(x)=\\var{c}\$

\n
\n
• $\\cos(x)=$ [[0]]
• \n
• $x=$ [[1]]$^\\circ$, [[2]]$^\\circ$, [[3]]$^\\circ$ or [[4]]$^\\circ$
• \n

\$\\var{b+1}\\cos(x)=-\\var{b-1}\$

\n
\n
• $\\cos(x)=$ [[0]]
• \n
• $x=$ [[1]]$^\\circ$, [[2]]$^\\circ$, [[3]]$^\\circ$ or [[4]]$^\\circ$
• \n

\$\\var{c+3}\\sin(x)=-\\var{c}\$

\n
\n
• $\\sin(x)=$ [[0]]
• \n
• $x=$ [[1]]$^\\circ$, [[2]]$^\\circ$, [[3]]$^\\circ$ or [[4]]$^\\circ$
• \n
• (Discard any solutions out of range.)
• \n
"}], "rulesets": {}, "statement": "

Solve the following equations in degrees, for $x$ in the range $0^\\circ\\leq x\\leq720^\\circ$.

\n

", "preamble": {"js": "", "css": ""}, "ungrouped_variables": [], "advice": "", "type": "question"}, {"name": "Trig equation, radians, simple", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Martin Jones", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/145/"}], "functions": {}, "ungrouped_variables": [], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "

\$\\var{a}\\sin(\\theta)=\\var{a-1}\$

\n
\n
• $\\sin(\\theta)=$ [[0]]
• \n
• $\\theta=$ [[1]] or [[2]]
• \n

\$\\var{b}\\cos(\\theta)=\\var{c}\$

\n
\n
• $\\cos(\\theta)=$ [[0]]
• \n
• $\\theta=$ [[1]] or [[2]]
• \n

\$\\var{c+3}\\sin(\\theta)=-\\var{c}\$

\n
\n
• $\\sin(\\theta)=$ [[0]]
• \n
• $\\theta=$ [[1]] or [[2]]
• \n
• (Discard any solutions out of range.)
• \n

\$\\var{b+1}\\cos(\\theta)=-\\var{b-1}\$

\n
\n
• $\\cos(\\theta)=$ [[0]]
• \n
• $\\theta=$ [[1]] or [[2]]
• \n

Solve the following equations in radians, for $\\theta$ in the range $0\\leq\\theta\\leq2\\pi$.

\n

", "variable_groups": [{"variables": ["a", "f1", "s1", "s11", "s12"], "name": "Q1"}, {"variables": ["b", "c", "f2", "s2", "s21", "s22"], "name": "Q2"}, {"variables": ["f3", "s31", "s32", "s3"], "name": "Q4"}, {"variables": ["f4", "s4", "s41", "s42"], "name": "Q3"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(3..9)", "templateType": "anything", "group": "Q1", "name": "a", "description": ""}, "f1": {"definition": "(a-1)/a", "templateType": "anything", "group": "Q1", "name": "f1", "description": ""}, "f2": {"definition": "c/b", "templateType": "anything", "group": "Q2", "name": "f2", "description": ""}, "f3": {"definition": "(1-b)/(b+1)", "templateType": "anything", "group": "Q4", "name": "f3", "description": ""}, "f4": {"definition": "-c/(c+3)", "templateType": "anything", "group": "Q3", "name": "f4", "description": ""}, "s3": {"definition": "arccos(f3)", "templateType": "anything", "group": "Q4", "name": "s3", "description": ""}, "s2": {"definition": "arccos(f2)", "templateType": "anything", "group": "Q2", "name": "s2", "description": ""}, "s1": {"definition": "arcsin(f1)", "templateType": "anything", "group": "Q1", "name": "s1", "description": ""}, "s31": {"definition": "precround(s3,2)", "templateType": "anything", "group": "Q4", "name": "s31", "description": ""}, "c": {"definition": "random(2..b-1)", "templateType": "anything", "group": "Q2", "name": "c", "description": ""}, "s4": {"definition": "arcsin(f4)", "templateType": "anything", "group": "Q3", "name": "s4", "description": ""}, "s22": {"definition": "precround(2*pi-s2,2)", "templateType": "anything", "group": "Q2", "name": "s22", "description": ""}, "b": {"definition": "random(5..12)", "templateType": "anything", "group": "Q2", "name": "b", "description": ""}, "s41": {"definition": "precround(pi-s4,2)", "templateType": "anything", "group": "Q3", "name": "s41", "description": ""}, "s42": {"definition": "precround(2*pi+s4,2)", "templateType": "anything", "group": "Q3", "name": "s42", "description": ""}, "s12": {"definition": "precround(pi-s1,2)", "templateType": "anything", "group": "Q1", "name": "s12", "description": ""}, "s21": {"definition": "precround(s2,2)", "templateType": "anything", "group": "Q2", "name": "s21", "description": ""}, "s32": {"definition": "precround(2*pi-s3,2)", "templateType": "anything", "group": "Q4", "name": "s32", "description": ""}, "s11": {"definition": "precround(s1,2)", "templateType": "anything", "group": "Q1", "name": "s11", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "None specified"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Trig equation, degrees, cosine, medium", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Martin Jones", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/145/"}], "functions": {}, "ungrouped_variables": ["a", "a1", "a2", "a3", "a4", "b", "b1", "b2", "b3", "b4", "f", "p"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "

$\\cos(x-\\var{b})=$ [[0]]

", "marks": 0, "gaps": [{"allowFractions": true, "marks": 1, "maxValue": "{f}+0.01", "minValue": "{f}-0.01", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}, {"prompt": "

$x-\\var{b}=$ [[0]]$^\\circ$, [[1]]$^\\circ$, [[2]]$^\\circ$ or [[3]]$^\\circ$

", "marks": 0, "gaps": [{"allowFractions": false, "marks": 1, "maxValue": "{a1}+0.5", "minValue": "{a1}-0.5", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "marks": 1, "maxValue": "{a2}+0.5", "minValue": "{a2}-0.5", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "marks": 1, "maxValue": "{a3}+0.5", "minValue": "{a3}-0.5", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "marks": 1, "maxValue": "{a4}+0.5", "minValue": "{a4}-0.5", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}, {"prompt": "

$x=$ [[0]]$^\\circ$, [[1]]$^\\circ$, [[2]]$^\\circ$ or [[3]]$^\\circ$

", "marks": 0, "gaps": [{"allowFractions": false, "marks": 1, "maxValue": "{b1}+0.5", "minValue": "{b1}-0.5", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "marks": 1, "maxValue": "{b2}+0.5", "minValue": "{b2}-0.5", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "marks": 1, "maxValue": "{b3}+0.5", "minValue": "{b3}-0.5", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "marks": 1, "maxValue": "{b4}+0.5", "minValue": "{b4}-0.5", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}], "statement": "

Solve the following equation in degrees, for $x$ in the range $0^\\circ\\leq x\\leq720^\\circ$.

\n

\$\\var{a+1}\\cos(x-\\var{b})=\\var{a-2}\$

\n

", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(3..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "b4": {"definition": "a4+b", "templateType": "anything", "group": "Ungrouped variables", "name": "b4", "description": ""}, "b": {"definition": "random(10..p-5)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "f": {"definition": "(a-2)/(a+1)", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "a1": {"definition": "p", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "p": {"definition": "arccos(f)*180/pi", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "a3": {"definition": "360+p", "templateType": "anything", "group": "Ungrouped variables", "name": "a3", "description": ""}, "a2": {"definition": "360-p", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "a4": {"definition": "720-p", "templateType": "anything", "group": "Ungrouped variables", "name": "a4", "description": ""}, "b2": {"definition": "a2+b", "templateType": "anything", "group": "Ungrouped variables", "name": "b2", "description": ""}, "b3": {"definition": "a3+b", "templateType": "anything", "group": "Ungrouped variables", "name": "b3", "description": ""}, "b1": {"definition": "a1+b", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "None specified"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Trig equation, radians, sine, medium", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Martin Jones", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/145/"}], "functions": {}, "ungrouped_variables": ["a1", "a2", "a3", "a4", "b", "b1", "b2", "b3", "b4", "c", "d", "f", "p"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "

$\\sin(\\theta-\\var{d})=$ [[0]]

", "marks": 0, "gaps": [{"allowFractions": true, "marks": 1, "maxValue": "{f}+0.01", "minValue": "{f}-0.01", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}, {"prompt": "

$\\theta-\\var{d}=$ [[0]] , [[1]], [[2]] or [[3]]

", "marks": 0, "gaps": [{"allowFractions": false, "marks": 1, "maxValue": "{a1}+0.01", "minValue": "{a1}-0.01", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "marks": 1, "maxValue": "{a2}+0.01", "minValue": "{a2}-0.01", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "marks": 1, "maxValue": "{a3}+0.01", "minValue": "{a3}-0.01", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "marks": 1, "maxValue": "{a4}+0.01", "minValue": "{a4}-0.01", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}, {"prompt": "

$\\theta=$ [[0]] , [[1]], [[2]] or [[3]]

", "marks": 0, "gaps": [{"allowFractions": false, "marks": 1, "maxValue": "{b1}+0.01", "minValue": "{b1}-0.01", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "marks": 1, "maxValue": "{b2}+0.01", "minValue": "{b2}-0.01", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "marks": 1, "maxValue": "{b3}+0.01", "minValue": "{b3}-0.01", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "marks": 1, "maxValue": "{b4}+0.01", "minValue": "{b4}-0.01", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}], "statement": "

Solve the following equations in radians, for $\\theta$ in the range $0\\leq\\theta\\leq4\\pi$:

\n

\$\\var{b}\\sin(\\theta-\\var{d})=\\var{c}\$

\n

", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"b4": {"definition": "a4+d", "templateType": "anything", "group": "Ungrouped variables", "name": "b4", "description": ""}, "c": {"definition": "random(2..b-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(5..12)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(1..p+2 #0.1)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "f": {"definition": "c/b", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "a1": {"definition": "p", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "p": {"definition": "arcsin(f)", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "a3": {"definition": "2*pi+p", "templateType": "anything", "group": "Ungrouped variables", "name": "a3", "description": ""}, "a2": {"definition": "pi-p", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "a4": {"definition": "3*pi-p", "templateType": "anything", "group": "Ungrouped variables", "name": "a4", "description": ""}, "b2": {"definition": "a2+d", "templateType": "anything", "group": "Ungrouped variables", "name": "b2", "description": ""}, "b3": {"definition": "a3+d", "templateType": "anything", "group": "Ungrouped variables", "name": "b3", "description": ""}, "b1": {"definition": "a1+d", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "None specified"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Trig equation, degrees, sine, complex", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Martin Jones", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/145/"}], "functions": {}, "ungrouped_variables": ["a", "a1", "a2", "a3", "a4", "b", "b1", "b2", "b3", "b4", "f1", "p", "c1", "c2", "c3", "c4"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "

$\\sin(2x+\\var{b})=$ [[0]]

", "marks": 0, "gaps": [{"allowFractions": true, "marks": 1, "maxValue": "{f1}+0.01", "minValue": "{f1}-0.01", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}, {"prompt": "

$2x+\\var{b}=$ [[0]]$^\\circ$, [[1]]$^\\circ$, [[2]]$^\\circ$ or [[3]]$^\\circ$

", "marks": 0, "gaps": [{"allowFractions": false, "marks": 1, "maxValue": "{a1}+0.5", "minValue": "{a1}-0.5", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "marks": 1, "maxValue": "{a2}+0.5", "minValue": "{a2}-0.5", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "marks": 1, "maxValue": "{a3}+0.5", "minValue": "{a3}-0.5", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "marks": 1, "maxValue": "{a4}+0.5", "minValue": "{a4}-0.5", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}, {"prompt": "

$2x=$ [[0]]$^\\circ$, [[1]]$^\\circ$, [[2]]$^\\circ$ or [[3]]$^\\circ$

", "marks": 0, "gaps": [{"allowFractions": false, "marks": 1, "maxValue": "{b1}+0.5", "minValue": "{b1}-0.5", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "marks": 1, "maxValue": "{b2}+0.5", "minValue": "{b2}-0.5", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "marks": 1, "maxValue": "{b3}+0.5", "minValue": "{b3}-0.5", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "marks": 1, "maxValue": "{b4}+0.5", "minValue": "{b4}-0.5", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}, {"prompt": "

$x=$ [[0]]$^\\circ$, [[1]]$^\\circ$, [[2]]$^\\circ$ or [[3]]$^\\circ$

Solve the following equation in degrees, for $x$ in the range $0^\\circ\\leq x\\leq360^\\circ$.

\n

\$\\var{a-1}\\sin(2x+\\var{b})=\\var{a-2}\$

\n

", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(3..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "f1": {"definition": "(a-2)/(a-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "f1", "description": ""}, "b": {"definition": "random(10..p-5)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "a1": {"definition": "p", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "p": {"definition": "arcsin(f1)*180/pi", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "a3": {"definition": "360+p", "templateType": "anything", "group": "Ungrouped variables", "name": "a3", "description": ""}, "a2": {"definition": "180-p", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "a4": {"definition": "540-p", "templateType": "anything", "group": "Ungrouped variables", "name": "a4", "description": ""}, "b2": {"definition": "a2-b", "templateType": "anything", "group": "Ungrouped variables", "name": "b2", "description": ""}, "b3": {"definition": "a3-b", "templateType": "anything", "group": "Ungrouped variables", "name": "b3", "description": ""}, "c3": {"definition": "b3/2", "templateType": "anything", "group": "Ungrouped variables", "name": "c3", "description": ""}, "c2": {"definition": "b2/2", "templateType": "anything", "group": "Ungrouped variables", "name": "c2", "description": ""}, "b4": {"definition": "a4-b", "templateType": "anything", "group": "Ungrouped variables", "name": "b4", "description": ""}, "c4": {"definition": "b4/2", "templateType": "anything", "group": "Ungrouped variables", "name": "c4", "description": ""}, "c1": {"definition": "b1/2", "templateType": "anything", "group": "Ungrouped variables", "name": "c1", "description": ""}, "b1": {"definition": "a1-b", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "None specified"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Trig equation, radians, cosine, complex", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Martin Jones", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/145/"}], "functions": {}, "ungrouped_variables": ["a1", "a2", "a3", "a4", "b", "b1", "b2", "b3", "b4", "c", "c1", "c2", "c3", "c4", "d", "f", "p"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "

$\\cos(3\\theta+\\var{d})=$ [[0]]

", "marks": 0, "gaps": [{"allowFractions": true, "marks": 1, "maxValue": "{f}+0.01", "minValue": "{f}-0.01", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}, {"prompt": "

$3\\theta+\\var{d}=$ [[0]] , [[1]], [[2]] or [[3]]

", "marks": 0, "gaps": [{"allowFractions": false, "marks": 1, "maxValue": "{a1}+0.01", "minValue": "{a1}-0.01", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "marks": 1, "maxValue": "{a2}+0.01", "minValue": "{a2}-0.01", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "marks": 1, "maxValue": "{a3}+0.01", "minValue": "{a3}-0.01", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "marks": 1, "maxValue": "{a4}+0.01", "minValue": "{a4}-0.01", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}, {"prompt": "

$3\\theta=$ [[0]] , [[1]], [[2]] or [[3]]

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$\\theta=$ [[0]] , [[1]] or [[2]]

\n

(Discard any solutions not in range.)

Solve the following equations in radians, for $\\theta$ in the range $0\\leq\\theta\\leq\\pi$:

\n

\$\\var{b}\\cos(3\\theta+\\var{d})=\\var{c}\$

\n

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$\\sin^2{\\theta}=$ [[0]]

\n

(Give your answer as a fraction or correct to 2 decimal places.)

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$\\sin{\\theta}=$ [[0]] or [[1]]

\n

(Write the positive answer first; use 2 decimal places)

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To each of your answers above, apply inverse sine to obtain angles between 0° and 360°.

\n

From first answer, $\\theta=$ [[0]]° or [[2]]°

\n

From second answer, $\\theta=$ [[1]]° or [[3]]°

\n

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Solve the following equation in the range $0\\leq\\theta\\leq360°$:

\n

\$\\var{a}\\sin^2{\\theta}=\\var{b}\$

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$\\cos^2{\\theta}=$ [[0]]

\n

(Give your answer as a fraction or correct to 2 decimal places.)

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$\\cos{\\theta}=$ [[0]] or [[1]]

\n

(Write the positive answer first; use 2 decimal places)

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To each of your answers above, apply inverse cosine to obtain angles between $0$ and $2\\pi$.

\n

From first answer, $\\theta=$ [[0]]° or [[1]]°

\n

From second answer, $\\theta=$ [[2]]° or [[3]]°

\n

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Solve the following equation in the range $0\\leq\\theta\\leq2\\pi$:

\n

\$\\var{a}\\cos^2{\\theta}=\\var{b}\$

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A variety of trigonometric equations which can be solved using inverse operations.

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