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\\[\\var{a}\\sin(x)=\\var{a-1}\\]
\n$\\sin(x)=$ [[0]]
\n$x=$ [[1]]$^\\circ$, [[2]]$^\\circ$, [[3]]$^\\circ$ or [[4]]$^\\circ$
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\n$\\cos(x)=$ [[0]]
\n$x=$ [[1]]$^\\circ$, [[2]]$^\\circ$, [[3]]$^\\circ$ or [[4]]$^\\circ$
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\n$\\cos(x)=$ [[0]]
\n$x=$ [[1]]$^\\circ$, [[2]]$^\\circ$, [[3]]$^\\circ$ or [[4]]$^\\circ$
"}, {"variableReplacementStrategy": "originalfirst", "gaps": [{"variableReplacementStrategy": "originalfirst", "scripts": {}, "correctAnswerFraction": true, "showPrecisionHint": false, "maxValue": "{f4}+0.01", "variableReplacements": [], "type": "numberentry", "allowFractions": true, "showCorrectAnswer": true, "minValue": "{f4}-0.01", "marks": 1}, {"correctAnswerFraction": false, "maxValue": "{s41}", "showCorrectAnswer": true, "marks": 1, "integerAnswer": true, "integerPartialCredit": "100", "variableReplacementStrategy": "originalfirst", "scripts": {}, "showPrecisionHint": false, "variableReplacements": [], "type": "numberentry", "allowFractions": false, "minValue": "{s41}"}, {"correctAnswerFraction": false, "maxValue": "{s42}", "showCorrectAnswer": true, "marks": 1, "integerAnswer": true, "integerPartialCredit": "100", "variableReplacementStrategy": "originalfirst", "scripts": {}, "showPrecisionHint": false, "variableReplacements": [], "type": "numberentry", "allowFractions": false, "minValue": "{s42}"}, {"correctAnswerFraction": false, "maxValue": "{s43}", "showCorrectAnswer": true, "marks": 1, "integerAnswer": true, "integerPartialCredit": "100", "variableReplacementStrategy": "originalfirst", "scripts": {}, "showPrecisionHint": false, "variableReplacements": [], "type": "numberentry", "allowFractions": false, "minValue": "{s43}"}, {"correctAnswerFraction": false, "maxValue": "{s44}", "showCorrectAnswer": true, "marks": 1, "integerAnswer": true, "integerPartialCredit": "100", "variableReplacementStrategy": "originalfirst", "scripts": {}, "showPrecisionHint": false, "variableReplacements": [], "type": "numberentry", "allowFractions": false, "minValue": "{s44}"}], "scripts": {}, "showCorrectAnswer": true, "type": "gapfill", "marks": 0, "variableReplacements": [], "prompt": "\\[\\var{c+3}\\sin(x)=-\\var{c}\\]
\n$\\sin(x)=$ [[0]]
\n$x=$ [[1]]$^\\circ$, [[2]]$^\\circ$, [[3]]$^\\circ$ or [[4]]$^\\circ$
\nDiscard any solutions out of range.
"}], "name": "Trigonometric Equations 1 - Simple (Degrees)", "metadata": {"notes": "", "licence": "Creative Commons Attribution 4.0 International", "description": "Simple trig equations with degrees
"}, "statement": "Solve the following equations in degrees, for $x$ in the range $0^\\circ\\leq x\\leq720^\\circ$.
\nGive your answers correct to the nearest degree in ascending order.
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\nThen perform the appropriate inverse trigonometric function on both sides to find the argument.
\nFinally, if the argument is an equation or function of the variable you want to find, manipulate your results accordingly.
\nFor example, if the solutions for the argument of $\\sin(2x)=a$, where $a$ is a number or function, were found to be $46^\\circ$ and $134^\\circ$ within the given range, further operations would be necessary to find the solutions for $x$.
\nHere, the first results would be halved and $x$ would therefore be equal to $23^\\circ$ and $67^\\circ$.
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