solvefor x,T(6)=3.15cos(pi/6 x)+19.15

{ "query": { "display": "solve for $$x,\\:T\\left(6\\right)=3.15\\cos\\left(\\frac{π}{6}x\\right)+19.15$$", "symbolab_question": "SOLVE_FOR#solvefor x,T(6)=3.15\\cos(\\frac{π}{6}x)+19.15" }, "solution": { "level": "PERFORMED", "subject": "Trigonometry", "topic": "Trig Equations", "subTopic": "Trig Equations", "default": "x=\\frac{6\\arccos(\\frac{120T-383}{63})}{π}+12n,x=-\\frac{6\\arccos(\\frac{120T-383}{63})}{π}+12n", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$solve\\:for\\:x,\\:T\\left(6\\right)=3.15\\cos\\left(\\frac{π}{6}x\\right)+19.15{\\quad:\\quad}x=\\frac{6\\arccos\\left(\\frac{120T-383}{63}\\right)}{π}+12n,\\:x=-\\frac{6\\arccos\\left(\\frac{120T-383}{63}\\right)}{π}+12n$$", "input": "T\\left(6\\right)=3.15\\cos\\left(\\frac{π}{6}x\\right)+19.15", "steps": [ { "type": "step", "primary": "Switch sides", "result": "3.15\\cos\\left(\\frac{π}{6}x\\right)+19.15=T\\cdot\\:6" }, { "type": "interim", "title": "Multiply both sides by $$100$$", "input": "3.15\\cos\\left(\\frac{π}{6}x\\right)+19.15=T\\cdot\\:6", "result": "315\\cos\\left(\\frac{π}{6}x\\right)+1915=600T", "steps": [ { "type": "step", "primary": "To eliminate decimal points, multiply by 10 for every digit after the decimal point", "secondary": [ "There are $$2\\:$$digits to the right of the decimal point, therefore multiply by $$100$$" ], "result": "3.15\\cos\\left(\\frac{π}{6}x\\right)\\cdot\\:100+19.15\\cdot\\:100=T\\cdot\\:6\\cdot\\:100" }, { "type": "step", "primary": "Refine", "result": "315\\cos\\left(\\frac{π}{6}x\\right)+1915=600T" } ], "meta": { "interimType": "Multiply Both Sides Specific 1Eq", "gptData": "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" } }, { "type": "interim", "title": "Move $$1915\\:$$to the right side", "input": "315\\cos\\left(\\frac{π}{6}x\\right)+1915=600T", "result": "315\\cos\\left(\\frac{π}{6}x\\right)=600T-1915", "steps": [ { "type": "step", "primary": "Subtract $$1915$$ from both sides", "result": "315\\cos\\left(\\frac{π}{6}x\\right)+1915-1915=600T-1915" }, { "type": "step", "primary": "Simplify", "result": "315\\cos\\left(\\frac{π}{6}x\\right)=600T-1915" } ], "meta": { "interimType": "Move to the Right Title 1Eq", "gptData": "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" } }, { "type": "interim", "title": "Divide both sides by $$315$$", "input": "315\\cos\\left(\\frac{π}{6}x\\right)=600T-1915", "result": "\\cos\\left(\\frac{π}{6}x\\right)=\\frac{120T-383}{63}", "steps": [ { "type": "step", "primary": "Divide both sides by $$315$$", "result": "\\frac{315\\cos\\left(\\frac{π}{6}x\\right)}{315}=\\frac{600T}{315}-\\frac{1915}{315}" }, { "type": "interim", "title": "Simplify", "input": "\\frac{315\\cos\\left(\\frac{π}{6}x\\right)}{315}=\\frac{600T}{315}-\\frac{1915}{315}", "result": "\\cos\\left(\\frac{π}{6}x\\right)=\\frac{120T-383}{63}", "steps": [ { "type": "interim", "title": "Simplify $$\\frac{315\\cos\\left(\\frac{π}{6}x\\right)}{315}:{\\quad}\\cos\\left(\\frac{π}{6}x\\right)$$", "input": "\\frac{315\\cos\\left(\\frac{π}{6}x\\right)}{315}", "steps": [ { "type": "step", "primary": "Divide the numbers: $$\\frac{315}{315}=1$$", "result": "=\\cos\\left(\\frac{π}{6}x\\right)" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s741/4xRwG6AHMDdA0AW4Bg444Oq9o8lz5JT/KYv500XRT57phEO/65qbLuStH/j3ICUCWbkwGOY7PqKo3U/JLJXx16M8E8IGRVz1nDt+ES0XFYUPALcsuwsPqZYSdYCtY1sD7NfhsPe7eDHrmjY0mE8DwQcN28geUT7aUsumC7doY9+cKcOBYBAI8JKGN154f2Db9NkMmi1Vu2sqtOl/ydYmpXFf3SOUx+H18qfp3MLg=" } }, { "type": "interim", "title": "Simplify $$\\frac{600T}{315}-\\frac{1915}{315}:{\\quad}\\frac{120T-383}{63}$$", "input": "\\frac{600T}{315}-\\frac{1915}{315}", "steps": [ { "type": "step", "primary": "Apply rule $$\\frac{a}{c}\\pm\\frac{b}{c}=\\frac{a\\pm\\:b}{c}$$", "result": "=\\frac{600T-1915}{315}" }, { "type": "interim", "title": "Factor $$600T-1915:{\\quad}5\\left(120T-383\\right)$$", "input": "600T-1915", "result": "=\\frac{5\\left(120T-383\\right)}{315}", "steps": [ { "type": "step", "primary": "Rewrite as", "result": "=5\\cdot\\:120T-5\\cdot\\:383" }, { "type": "step", "primary": "Factor out common term $$5$$", "result": "=5\\left(120T-383\\right)", "meta": { "practiceLink": "/practice/factoring-practice", "practiceTopic": "Factoring" } } ], "meta": { "interimType": "Algebraic Manipulation Factor Title 1Eq" } }, { "type": "step", "primary": "Cancel the common factor: $$5$$", "result": "=\\frac{120T-383}{63}" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7DzFS7fbZu8x1rzkbX0Py3msf2Eu3DrckVKEhDr4eW9qlns2rx1H1jFhQun4MTqkkcJChiVhDxT5N/LHSTLMjyHXu8mnqhb3Ajl6ErEnS6hnLJ9+fQIktoqA3AoJBNzMjHjb2+5NLFZrsH9fcPWg/TcBZCZf4UBlDnt5DwfBsIkLrYYWP917hUSsClAcTVhHW1UxtWYg0WAGwxxDGQ31oPw==" } }, { "type": "step", "result": "\\cos\\left(\\frac{π}{6}x\\right)=\\frac{120T-383}{63}" } ], "meta": { "interimType": "Generic Simplify 0Eq" } } ], "meta": { "interimType": "Divide Both Sides Specific 1Eq", "gptData": "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" } }, { "type": "interim", "title": "Apply trig inverse properties", "input": "\\cos\\left(\\frac{π}{6}x\\right)=\\frac{120T-383}{63}", "result": "\\frac{π}{6}x=\\arccos\\left(\\frac{120T-383}{63}\\right)+2πn,\\:\\frac{π}{6}x=-\\arccos\\left(\\frac{120T-383}{63}\\right)+2πn", "steps": [ { "type": "step", "primary": "General solutions for $$\\cos\\left(\\frac{π}{6}x\\right)=\\frac{120T-383}{63}$$", "secondary": [ "$$\\cos\\left(x\\right)=a\\quad\\Rightarrow\\quad\\:x=\\arccos\\left(a\\right)+2πn,\\:\\quad\\:x=-\\arccos\\left(a\\right)+2πn$$" ], "result": "\\frac{π}{6}x=\\arccos\\left(\\frac{120T-383}{63}\\right)+2πn,\\:\\frac{π}{6}x=-\\arccos\\left(\\frac{120T-383}{63}\\right)+2πn" } ], "meta": { "interimType": "Trig Apply Inverse Props 0Eq" } }, { "type": "interim", "title": "Solve $$\\frac{π}{6}x=\\arccos\\left(\\frac{120T-383}{63}\\right)+2πn:{\\quad}x=\\frac{6\\arccos\\left(\\frac{120T-383}{63}\\right)}{π}+12n$$", "input": "\\frac{π}{6}x=\\arccos\\left(\\frac{120T-383}{63}\\right)+2πn", "steps": [ { "type": "interim", "title": "Multiply both sides by $$6$$", "input": "\\frac{π}{6}x=\\arccos\\left(\\frac{120T-383}{63}\\right)+2πn", "result": "πx=6\\arccos\\left(\\frac{120T-383}{63}\\right)+12πn", "steps": [ { "type": "step", "primary": "Multiply both sides by $$6$$", "result": "6\\cdot\\:\\frac{π}{6}x=6\\arccos\\left(\\frac{120T-383}{63}\\right)+6\\cdot\\:2πn" }, { "type": "interim", "title": "Simplify", "input": "6\\cdot\\:\\frac{π}{6}x=6\\arccos\\left(\\frac{120T-383}{63}\\right)+6\\cdot\\:2πn", "result": "πx=6\\arccos\\left(\\frac{120T-383}{63}\\right)+12πn", "steps": [ { "type": "interim", "title": "Simplify $$6\\cdot\\:\\frac{π}{6}x:{\\quad}πx$$", "input": "6\\cdot\\:\\frac{π}{6}x", "steps": [ { "type": "step", "primary": "Multiply fractions: $$a\\cdot\\frac{b}{c}=\\frac{a\\:\\cdot\\:b}{c}$$", "result": "=\\frac{6π}{6}x" }, { "type": "step", "primary": "Cancel the common factor: $$6$$", "result": "=xπ" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7wHsyNILr7YqAxQ7kxdsiXp80kQDaoc2bzKea2U55oCN1g99dC9fj9sg0EHzBIRDRM/IK15PU5ovk7AtQZ+s8oXql8XXPq6bNQlMm+36iNhmQlvSOtTjyey50aWEaY7D9VdG+Z3I7I3+MVNRn4WdFuVVNr95/erXYFBeyX172Jjk=" } }, { "type": "interim", "title": "Simplify $$6\\arccos\\left(\\frac{120T-383}{63}\\right)+6\\cdot\\:2πn:{\\quad}6\\arccos\\left(\\frac{120T-383}{63}\\right)+12πn$$", "input": "6\\arccos\\left(\\frac{120T-383}{63}\\right)+6\\cdot\\:2πn", "steps": [ { "type": "step", "primary": "Multiply the numbers: $$6\\cdot\\:2=12$$", "result": "=6\\arccos\\left(\\frac{120T-383}{63}\\right)+12πn" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7p2hwmoMKLha/PWkR/4PiLywHOSBGGMN+7paf7DutLQ44yMzFsWNOQrdFyyNxtzgQVdNK6b/PmQukzNdLVQkh7Hi9dbZ5yDMOmgrM+UqIK5ABa9FMaW/dncSH5PYc2YQMJh5vnAW6sqnNr3ab4xqJ/D/L0MoYg+CUn6oyL3EO7YppEjsYKnQdDP7MPDbdrF10+65AR46LztRAMcDrOMlbRtNHH3rG9SW9LaBPE7SpBEW8sYeqxmVneNcCuMVEsWTzvzIPeEtDfcHv/z8uls8Teg==" } }, { "type": "step", "result": "πx=6\\arccos\\left(\\frac{120T-383}{63}\\right)+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": "πx=6\\arccos\\left(\\frac{120T-383}{63}\\right)+12πn", "result": "x=\\frac{6\\arccos\\left(\\frac{120T-383}{63}\\right)}{π}+12n", "steps": [ { "type": "step", "primary": "Divide both sides by $$π$$", "result": "\\frac{πx}{π}=\\frac{6\\arccos\\left(\\frac{120T-383}{63}\\right)}{π}+\\frac{12πn}{π}" }, { "type": "step", "primary": "Simplify", "result": "x=\\frac{6\\arccos\\left(\\frac{120T-383}{63}\\right)}{π}+12n" } ], "meta": { "interimType": "Divide Both Sides Specific 1Eq", "gptData": 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"interim", "title": "Solve $$\\frac{π}{6}x=-\\arccos\\left(\\frac{120T-383}{63}\\right)+2πn:{\\quad}x=-\\frac{6\\arccos\\left(\\frac{120T-383}{63}\\right)}{π}+12n$$", "input": "\\frac{π}{6}x=-\\arccos\\left(\\frac{120T-383}{63}\\right)+2πn", "steps": [ { "type": "interim", "title": "Multiply both sides by $$6$$", "input": "\\frac{π}{6}x=-\\arccos\\left(\\frac{120T-383}{63}\\right)+2πn", "result": "πx=-6\\arccos\\left(\\frac{120T-383}{63}\\right)+12πn", "steps": [ { "type": "step", "primary": "Multiply both sides by $$6$$", "result": "6\\cdot\\:\\frac{π}{6}x=-6\\arccos\\left(\\frac{120T-383}{63}\\right)+6\\cdot\\:2πn" }, { "type": "interim", "title": "Simplify", "input": "6\\cdot\\:\\frac{π}{6}x=-6\\arccos\\left(\\frac{120T-383}{63}\\right)+6\\cdot\\:2πn", "result": "πx=-6\\arccos\\left(\\frac{120T-383}{63}\\right)+12πn", "steps": [ { "type": "interim", "title": "Simplify $$6\\cdot\\:\\frac{π}{6}x:{\\quad}πx$$", "input": "6\\cdot\\:\\frac{π}{6}x", "steps": [ { "type": "step", "primary": "Multiply fractions: $$a\\cdot\\frac{b}{c}=\\frac{a\\:\\cdot\\:b}{c}$$", "result": "=\\frac{6π}{6}x" }, { "type": "step", "primary": "Cancel the common factor: $$6$$", "result": "=xπ" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7wHsyNILr7YqAxQ7kxdsiXp80kQDaoc2bzKea2U55oCN1g99dC9fj9sg0EHzBIRDRM/IK15PU5ovk7AtQZ+s8oXql8XXPq6bNQlMm+36iNhmQlvSOtTjyey50aWEaY7D9VdG+Z3I7I3+MVNRn4WdFuVVNr95/erXYFBeyX172Jjk=" } }, { "type": "interim", "title": "Simplify $$-6\\arccos\\left(\\frac{120T-383}{63}\\right)+6\\cdot\\:2πn:{\\quad}-6\\arccos\\left(\\frac{120T-383}{63}\\right)+12πn$$", "input": "-6\\arccos\\left(\\frac{120T-383}{63}\\right)+6\\cdot\\:2πn", "steps": [ { "type": "step", "primary": "Multiply the numbers: $$6\\cdot\\:2=12$$", "result": "=-6\\arccos\\left(\\frac{120T-383}{63}\\right)+12πn" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7neiLU7Oa4dRWcIjjBMSLRtNHH3rG9SW9LaBPE7SpBEUrY6P1u4JbGiO/sVj6ezjiLTrWWMFI8l4Q07DZ5+hJa73ahJ5PBGDK/yyCw4BnJcwNI0Zu2yFr6+U/MWJgkizL5IxqN+Z0ujax/y4J9pQd8VaoszjYHFPTN6tjxnkfaKceKYFFhGodJZ4mS5Q+F9MLgv7c49/6wJhGZ1lGKrz8ORu9dqJdJXZV4cR9zEAkWhMD04KxWlUT6DIIwIVnz7RkRRHxPuhd41B+Skam5GV5WA==" } }, { "type": "step", "result": "πx=-6\\arccos\\left(\\frac{120T-383}{63}\\right)+12πn" } ], "meta": { "interimType": "Generic Simplify 0Eq" } } ], "meta": { "interimType": "Multiply Both Sides Specific 1Eq", "gptData": 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"πx=-6\\arccos\\left(\\frac{120T-383}{63}\\right)+12πn", "result": "x=-\\frac{6\\arccos\\left(\\frac{120T-383}{63}\\right)}{π}+12n", "steps": [ { "type": "step", "primary": "Divide both sides by $$π$$", "result": "\\frac{πx}{π}=-\\frac{6\\arccos\\left(\\frac{120T-383}{63}\\right)}{π}+\\frac{12πn}{π}" }, { "type": "step", "primary": "Simplify", "result": "x=-\\frac{6\\arccos\\left(\\frac{120T-383}{63}\\right)}{π}+12n" } ], "meta": { "interimType": "Divide Both Sides Specific 1Eq", "gptData": 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"step", "result": "x=\\frac{6\\arccos\\left(\\frac{120T-383}{63}\\right)}{π}+12n,\\:x=-\\frac{6\\arccos\\left(\\frac{120T-383}{63}\\right)}{π}+12n" } ], "meta": { "solvingClass": "Trig Equations", "practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Trig%20Equations", "practiceTopic": "Trig Equations" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "T(6)-3.15\\cos(\\frac{π}{6}x)-19.15" }, "showViewLarger": true } }, "meta": { "showVerify": true } }