solvefor x,2sin((pi(x-2))/6)=1

{ "query": { "display": "solve for $$x,\\:2\\sin\\left(\\frac{π\\left(x-2\\right)}{6}\\right)=1$$", "symbolab_question": "SOLVE_FOR#solvefor x,2\\sin(\\frac{π(x-2)}{6})=1" }, "solution": { "level": "PERFORMED", "subject": "Trigonometry", "topic": "Trig Equations", "subTopic": "Trig Equations", "default": "x=12n+3,x=12n+7", "degrees": "x=171.88733…^{\\circ }+687.54935…^{\\circ }n,x=401.07045…^{\\circ }+687.54935…^{\\circ }n", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$solve\\:for\\:x,\\:2\\sin\\left(\\frac{π\\left(x-2\\right)}{6}\\right)=1{\\quad:\\quad}x=12n+3,\\:x=12n+7$$", "input": "2\\sin\\left(\\frac{π\\left(x-2\\right)}{6}\\right)=1", "steps": [ { "type": "interim", "title": "Divide both sides by $$2$$", "input": "2\\sin\\left(\\frac{π\\left(x-2\\right)}{6}\\right)=1", "result": "\\sin\\left(\\frac{π\\left(x-2\\right)}{6}\\right)=\\frac{1}{2}", "steps": [ { "type": "step", "primary": "Divide both sides by $$2$$", "result": "\\frac{2\\sin\\left(\\frac{π\\left(x-2\\right)}{6}\\right)}{2}=\\frac{1}{2}" }, { "type": "step", "primary": "Simplify", "result": "\\sin\\left(\\frac{π\\left(x-2\\right)}{6}\\right)=\\frac{1}{2}" } ], "meta": { "interimType": "Divide Both Sides Specific 1Eq", "gptData": "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" } }, { "type": "interim", "title": "General solutions for $$\\sin\\left(\\frac{π\\left(x-2\\right)}{6}\\right)=\\frac{1}{2}$$", "result": "\\frac{π\\left(x-2\\right)}{6}=\\frac{π}{6}+2πn,\\:\\frac{π\\left(x-2\\right)}{6}=\\frac{5π}{6}+2πn", "steps": [ { "type": "step", "primary": "$$\\sin\\left(x\\right)$$ periodicity table with $$2πn$$ cycle:<br/>$$\\begin{array}{|c|c|c|c|}\\hline x&\\sin(x)&x&\\sin(x)\\\\\\hline 0&0&π&0\\\\\\hline \\frac{π}{6}&\\frac{1}{2}&\\frac{7π}{6}&-\\frac{1}{2}\\\\\\hline \\frac{π}{4}&\\frac{\\sqrt{2}}{2}&\\frac{5π}{4}&-\\frac{\\sqrt{2}}{2}\\\\\\hline \\frac{π}{3}&\\frac{\\sqrt{3}}{2}&\\frac{4π}{3}&-\\frac{\\sqrt{3}}{2}\\\\\\hline \\frac{π}{2}&1&\\frac{3π}{2}&-1\\\\\\hline \\frac{2π}{3}&\\frac{\\sqrt{3}}{2}&\\frac{5π}{3}&-\\frac{\\sqrt{3}}{2}\\\\\\hline \\frac{3π}{4}&\\frac{\\sqrt{2}}{2}&\\frac{7π}{4}&-\\frac{\\sqrt{2}}{2}\\\\\\hline \\frac{5π}{6}&\\frac{1}{2}&\\frac{11π}{6}&-\\frac{1}{2}\\\\\\hline \\end{array}$$" }, { "type": "step", "result": "\\frac{π\\left(x-2\\right)}{6}=\\frac{π}{6}+2πn,\\:\\frac{π\\left(x-2\\right)}{6}=\\frac{5π}{6}+2πn" } ], "meta": { "interimType": "Trig General Solutions sin 1Eq" } }, { "type": "interim", "title": "Solve $$\\frac{π\\left(x-2\\right)}{6}=\\frac{π}{6}+2πn:{\\quad}x=12n+3$$", "input": "\\frac{π\\left(x-2\\right)}{6}=\\frac{π}{6}+2πn", "steps": [ { "type": "interim", "title": "Multiply both sides by $$6$$", "input": "\\frac{π\\left(x-2\\right)}{6}=\\frac{π}{6}+2πn", "result": "π\\left(x-2\\right)=π+12πn", "steps": [ { "type": "step", "primary": "Multiply both sides by $$6$$", "result": "\\frac{6π\\left(x-2\\right)}{6}=6\\cdot\\:\\frac{π}{6}+6\\cdot\\:2πn" }, { "type": "interim", "title": "Simplify", "input": "\\frac{6π\\left(x-2\\right)}{6}=6\\cdot\\:\\frac{π}{6}+6\\cdot\\:2πn", "result": "π\\left(x-2\\right)=π+12πn", "steps": [ { "type": "interim", "title": "Simplify $$\\frac{6π\\left(x-2\\right)}{6}:{\\quad}π\\left(x-2\\right)$$", "input": "\\frac{6π\\left(x-2\\right)}{6}", "steps": [ { "type": "step", "primary": "Divide the numbers: $$\\frac{6}{6}=1$$", "result": "=π\\left(x-2\\right)" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s79ejiHkH5jG44C5zGseaHgdGomS3dOHHl3kO1dZEqjY5wkKGJWEPFPk38sdJMsyPIVC8WbGpNQpKTi9U95igzQdbA+zX4bD3u3gx65o2NJhPA8EHDdvIHlE+2lLLpgu3aX57ucY1TgTfoPj+xz308Sr8yD3hLQ33B7/8/LpbPE3o=" } }, { "type": "interim", "title": "Simplify $$6\\cdot\\:\\frac{π}{6}+6\\cdot\\:2πn:{\\quad}π+12πn$$", "input": "6\\cdot\\:\\frac{π}{6}+6\\cdot\\:2πn", "steps": [ { "type": "interim", "title": "$$6\\cdot\\:\\frac{π}{6}=π$$", "input": "6\\cdot\\:\\frac{π}{6}", "steps": [ { "type": "step", "primary": "Multiply fractions: $$a\\cdot\\frac{b}{c}=\\frac{a\\:\\cdot\\:b}{c}$$", "result": "=\\frac{π6}{6}" }, { "type": "step", "primary": "Cancel the common factor: $$6$$", "result": "=π" } ], "meta": { "solvingClass": "Solver", "interimType": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7wHsyNILr7YqAxQ7kxdsiXjqt2Xgtb3t95fujkffGgBwJQJZuTAY5js+oqjdT8ksl58bIKwWzS3dUPXOsTsmj0o1zGcaO4jwf1MYQ1lVbGjthmOq3nKs2sHwkU4yPT0tfJLd1ohke2Wgml78++2zI0g==" } }, { "type": "interim", "title": "$$6\\cdot\\:2πn=12πn$$", "input": "6\\cdot\\:2πn", "steps": [ { "type": "step", "primary": "Multiply the numbers: $$6\\cdot\\:2=12$$", "result": "=12πn" } ], "meta": { "solvingClass": "Solver", "interimType": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7bz20bx0y+QZAG1CBUuArRVXTSum/z5kLpMzXS1UJIew0P+GU+4m2h2otW1TtPWGbP8vQyhiD4JSfqjIvcQ7tii9cwWc6UP9J1v42F03+dadFEfE+6F3jUH5KRqbkZXlY" } }, { "type": "step", "result": "=π+12πn" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7wHsyNILr7YqAxQ7kxdsiXq7PliNITDcJSY0yVKDKwO3+n/+FjN833TADO2gxs6I7zMFYmi1F5Hg/ibpEToVnY0TdWThU6Eixr57UWrJmD8bWwPs1+Gw97t4MeuaNjSYTNLSPl5gqG7gqymrd0rTjTBNK2eDuWLCwYHNMWEds3LwIYvi+IKEA9+ss0nmKu+QFJLd1ohke2Wgml78++2zI0g==" } }, { "type": "step", "result": "π\\left(x-2\\right)=π+12πn" } ], "meta": { "interimType": "Generic Simplify 0Eq" } } ], "meta": { "interimType": "Multiply Both Sides Specific 1Eq", "gptData": "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" } }, { "type": "interim", "title": "Divide both sides by $$π$$", "input": "π\\left(x-2\\right)=π+12πn", "result": "x-2=1+12n", "steps": [ { "type": "step", "primary": "Divide both sides by $$π$$", "result": "\\frac{π\\left(x-2\\right)}{π}=\\frac{π}{π}+\\frac{12πn}{π}" }, { "type": "interim", "title": "Simplify", "input": "\\frac{π\\left(x-2\\right)}{π}=\\frac{π}{π}+\\frac{12πn}{π}", "result": "x-2=1+12n", "steps": [ { "type": "interim", "title": "Simplify $$\\frac{π\\left(x-2\\right)}{π}:{\\quad}x-2$$", "input": "\\frac{π\\left(x-2\\right)}{π}", "steps": [ { "type": "step", "primary": "Cancel the common factor: $$π$$", "result": "=x-2" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7I7qjUVjffLCBgaqzUSd1w/2V78es4+ZD9eMofuQrDWBwkKGJWEPFPk38sdJMsyPI6o9yM0RIauF1R3xyjMmDh4saY2cs9YZ/08feWmaOgkhsJD0xzQNiY+E+IZ6J4M1XnO8v9YOeYme8VbQShFmtcw==" } }, { "type": "interim", "title": "Simplify $$\\frac{π}{π}+\\frac{12πn}{π}:{\\quad}1+12n$$", "input": "\\frac{π}{π}+\\frac{12πn}{π}", "steps": [ { "type": "step", "primary": "Apply rule $$\\frac{a}{a}=1$$", "secondary": [ "$$\\frac{π}{π}=1$$" ], "result": "=1+\\frac{12πn}{π}" }, { "type": "interim", "title": "Cancel $$\\frac{12πn}{π}:{\\quad}12n$$", "input": "\\frac{12πn}{π}", "steps": [ { "type": "step", "primary": "Cancel the common factor: $$π$$", "result": "=12n" } ], "meta": { "interimType": "Generic Cancel Title 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s79Kg+idP5vLVrjUll6eMdYjzF++8ldgAFNjMtUkNTBhHdd47a0hQ8flDbGsI5To1dpoZwL7EoLhVnYFDUqSFwDtbA+zX4bD3u3gx65o2NJhNifyQFjyUJIsQsMU1ZJWYTzRbGnN3YX7ddiCzloyL94Q==" } }, { "type": "step", "result": "=1+12n" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7NHT3/d1+cFJ6h7isZICldZCocXSnD5thR/gg0bfrclV8JUsz2KlvHkr3DU5Bm41JY2azjPkPCRG2cjooPAbcsvdmOcvefG3N31s/Ol8R37SY3ASC+aZqPN1DBWUUsybFFwfa0e/tlC4FY8+RKRvPhGcjZFk2RHxQBUGjRHjqBQa8LTrtrrjU0QhwbsmIxtoe" } }, { "type": "step", "result": "x-2=1+12n" } ], "meta": { "interimType": "Generic Simplify 0Eq" } } ], "meta": { "interimType": "Divide Both Sides Specific 1Eq", "gptData": "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" } }, { "type": "interim", "title": "Move $$2\\:$$to the right side", "input": "x-2=1+12n", "result": "x=12n+3", "steps": [ { "type": "step", "primary": "Add $$2$$ to both sides", "result": "x-2+2=1+12n+2" }, { "type": "step", "primary": "Simplify", "result": "x=12n+3" } ], "meta": { "interimType": "Move to the Right Title 1Eq", "gptData": "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" } } ], "meta": { "solvingClass": "Equations", "interimType": "Generic Solve Title 1Eq" } }, { "type": "interim", "title": "Solve $$\\frac{π\\left(x-2\\right)}{6}=\\frac{5π}{6}+2πn:{\\quad}x=12n+7$$", "input": "\\frac{π\\left(x-2\\right)}{6}=\\frac{5π}{6}+2πn", "steps": [ { "type": "interim", "title": "Multiply both sides by $$6$$", "input": "\\frac{π\\left(x-2\\right)}{6}=\\frac{5π}{6}+2πn", "result": "π\\left(x-2\\right)=5π+12πn", "steps": [ { "type": "step", "primary": "Multiply both sides by $$6$$", "result": "\\frac{6π\\left(x-2\\right)}{6}=6\\cdot\\:\\frac{5π}{6}+6\\cdot\\:2πn" }, { "type": "interim", "title": "Simplify", "input": "\\frac{6π\\left(x-2\\right)}{6}=6\\cdot\\:\\frac{5π}{6}+6\\cdot\\:2πn", "result": "π\\left(x-2\\right)=5π+12πn", "steps": [ { "type": "interim", "title": "Simplify $$\\frac{6π\\left(x-2\\right)}{6}:{\\quad}π\\left(x-2\\right)$$", "input": "\\frac{6π\\left(x-2\\right)}{6}", "steps": [ { "type": "step", "primary": "Divide the numbers: $$\\frac{6}{6}=1$$", "result": "=π\\left(x-2\\right)" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s79ejiHkH5jG44C5zGseaHgdGomS3dOHHl3kO1dZEqjY5wkKGJWEPFPk38sdJMsyPIVC8WbGpNQpKTi9U95igzQdbA+zX4bD3u3gx65o2NJhPA8EHDdvIHlE+2lLLpgu3aX57ucY1TgTfoPj+xz308Sr8yD3hLQ33B7/8/LpbPE3o=" } }, { "type": "interim", "title": "Simplify $$6\\cdot\\:\\frac{5π}{6}+6\\cdot\\:2πn:{\\quad}5π+12πn$$", "input": "6\\cdot\\:\\frac{5π}{6}+6\\cdot\\:2πn", "steps": [ { "type": "interim", "title": "$$6\\cdot\\:\\frac{5π}{6}=5π$$", "input": "6\\cdot\\:\\frac{5π}{6}", "steps": [ { "type": "step", "primary": "Multiply fractions: $$a\\cdot\\frac{b}{c}=\\frac{a\\:\\cdot\\:b}{c}$$", "result": "=\\frac{5π6}{6}" }, { "type": "step", "primary": "Cancel the common factor: $$6$$", "result": "=5π" } ], "meta": { "solvingClass": "Solver", "interimType": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7wHsyNILr7YqAxQ7kxdsiXhfSMm0qrPdKn557Lx5c4c91g99dC9fj9sg0EHzBIRDR/vFTybheNsvazJfQjKcGUe0CRy+2L4OBzM+Wl4djjIHImxy6oMWx2ujfRKeYv3flG6Jn6ojVoz2IDd0XmrUm3Q==" } }, { "type": "interim", "title": "$$6\\cdot\\:2πn=12πn$$", "input": "6\\cdot\\:2πn", "steps": [ { "type": "step", "primary": "Multiply the numbers: $$6\\cdot\\:2=12$$", "result": "=12πn" } ], "meta": { "solvingClass": "Solver", "interimType": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7bz20bx0y+QZAG1CBUuArRVXTSum/z5kLpMzXS1UJIew0P+GU+4m2h2otW1TtPWGbP8vQyhiD4JSfqjIvcQ7tii9cwWc6UP9J1v42F03+dadFEfE+6F3jUH5KRqbkZXlY" } }, { "type": "step", "result": "=5π+12πn" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7wHsyNILr7YqAxQ7kxdsiXg84jEBHssn4cC84MO8lByXj+O38RAvKhZolrKec34mYcJChiVhDxT5N/LHSTLMjyHBUv49NdIYvBoxY2t+oWDKBBTEk/JQ2cZ9WKuRzClU7uKVEDZEBxWaTLJyCMglNdTo1ZZfACLFWhjkWidV4CJE6Xy0JYqqR2PYTuSHKJ8rOuW7ftHJHwkhBWASHRi462g==" } }, { "type": "step", "result": "π\\left(x-2\\right)=5π+12πn" } ], "meta": { "interimType": "Generic Simplify 0Eq" } } ], "meta": { "interimType": "Multiply Both Sides Specific 1Eq", "gptData": 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"\\frac{π\\left(x-2\\right)}{π}=\\frac{5π}{π}+\\frac{12πn}{π}" }, { "type": "interim", "title": "Simplify", "input": "\\frac{π\\left(x-2\\right)}{π}=\\frac{5π}{π}+\\frac{12πn}{π}", "result": "x-2=5+12n", "steps": [ { "type": "interim", "title": "Simplify $$\\frac{π\\left(x-2\\right)}{π}:{\\quad}x-2$$", "input": "\\frac{π\\left(x-2\\right)}{π}", "steps": [ { "type": "step", "primary": "Cancel the common factor: $$π$$", "result": "=x-2" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7I7qjUVjffLCBgaqzUSd1w/2V78es4+ZD9eMofuQrDWBwkKGJWEPFPk38sdJMsyPI6o9yM0RIauF1R3xyjMmDh4saY2cs9YZ/08feWmaOgkhsJD0xzQNiY+E+IZ6J4M1XnO8v9YOeYme8VbQShFmtcw==" } }, { "type": "interim", "title": "Simplify $$\\frac{5π}{π}+\\frac{12πn}{π}:{\\quad}5+12n$$", "input": "\\frac{5π}{π}+\\frac{12πn}{π}", "steps": [ { "type": "interim", "title": "Cancel $$\\frac{5π}{π}:{\\quad}5$$", "input": "\\frac{5π}{π}", "steps": [ { "type": "step", "primary": "Cancel the common factor: $$π$$", "result": "=5" } ], "meta": { "interimType": "Generic Cancel Title 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s79Kg+idP5vLVrjUll6eMdYuyUOAzJWVed+B1KcmevyB8DnzlbPZjyKgy1eUCFsLd5qbyiE1UNaMyOSzE0Ofpba7S+s697jzDrK7YR+xVFN86U31iAaaYN2Lc2RD6/xhHP8FVsYr++bScvtYtsCxP0xA==" } }, { "type": "step", "result": "=5+\\frac{12πn}{π}" }, { "type": "interim", "title": "Cancel $$\\frac{12πn}{π}:{\\quad}12n$$", "input": "\\frac{12πn}{π}", "steps": [ { "type": "step", "primary": "Cancel the common factor: $$π$$", "result": "=12n" } ], "meta": { "interimType": "Generic Cancel Title 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s79Kg+idP5vLVrjUll6eMdYjzF++8ldgAFNjMtUkNTBhHdd47a0hQ8flDbGsI5To1dpoZwL7EoLhVnYFDUqSFwDtbA+zX4bD3u3gx65o2NJhNifyQFjyUJIsQsMU1ZJWYTzRbGnN3YX7ddiCzloyL94Q==" } }, { "type": "step", "result": "=5+12n" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s72h+wsiHchrITxi89uhFfqmRRNqUem6NxPAJDqVYHUl9Y8AEv4uUdq9OFaJuQYiSNo5FYteSPKwXny4uCMrdsKxrz1/F6exksd1qv+pkv0oOLGmNnLPWGf9PH3lpmjoJI1oQMMLckMupd3/EMO7UyLkT/0uahm+9Te4NACIfYBDvmztGYqiaV2vO90ZyMx9WG" } }, { "type": "step", "result": "x-2=5+12n" } ], "meta": { "interimType": "Generic Simplify 0Eq" } } ], "meta": { "interimType": "Divide Both Sides Specific 1Eq", "gptData": 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