10sin(20t-pi/6)=8

{ "query": { "display": "$$10\\sin\\left(20t-\\frac{π}{6}\\right)=8$$", "symbolab_question": "EQUATION#10\\sin(20t-\\frac{π}{6})=8" }, "solution": { "level": "PERFORMED", "subject": "Trigonometry", "topic": "Trig Equations", "subTopic": "Trig Equations", "default": "t=\\frac{πn}{10}+\\frac{π}{120}+\\frac{0.92729…}{20},t=\\frac{π}{20}+\\frac{π}{120}+\\frac{πn}{10}-\\frac{0.92729…}{20}", "degrees": "t=4.15650…^{\\circ }+18^{\\circ }n,t=7.84349…^{\\circ }+18^{\\circ }n", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$10\\sin\\left(20t-\\frac{π}{6}\\right)=8{\\quad:\\quad}t=\\frac{πn}{10}+\\frac{π}{120}+\\frac{0.92729…}{20},\\:t=\\frac{π}{20}+\\frac{π}{120}+\\frac{πn}{10}-\\frac{0.92729…}{20}$$", "input": "10\\sin\\left(20t-\\frac{π}{6}\\right)=8", "steps": [ { "type": "interim", "title": "Divide both sides by $$10$$", "input": "10\\sin\\left(20t-\\frac{π}{6}\\right)=8", "result": "\\sin\\left(20t-\\frac{π}{6}\\right)=\\frac{4}{5}", "steps": [ { "type": "step", "primary": "Divide both sides by $$10$$", "result": "\\frac{10\\sin\\left(20t-\\frac{π}{6}\\right)}{10}=\\frac{8}{10}" }, { "type": "step", "primary": "Simplify", "result": "\\sin\\left(20t-\\frac{π}{6}\\right)=\\frac{4}{5}" } ], "meta": { "interimType": "Divide Both Sides Specific 1Eq", "gptData": "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" } }, { "type": "interim", "title": "Apply trig inverse properties", "input": "\\sin\\left(20t-\\frac{π}{6}\\right)=\\frac{4}{5}", "result": "20t-\\frac{π}{6}=\\arcsin\\left(\\frac{4}{5}\\right)+2πn,\\:20t-\\frac{π}{6}=π-\\arcsin\\left(\\frac{4}{5}\\right)+2πn", "steps": [ { "type": "step", "primary": "General solutions for $$\\sin\\left(20t-\\frac{π}{6}\\right)=\\frac{4}{5}$$", "secondary": [ "$$\\sin\\left(x\\right)=a\\quad\\Rightarrow\\quad\\:x=\\arcsin\\left(a\\right)+2πn,\\:\\quad\\:x=π-\\arcsin\\left(a\\right)+2πn$$" ], "result": "20t-\\frac{π}{6}=\\arcsin\\left(\\frac{4}{5}\\right)+2πn,\\:20t-\\frac{π}{6}=π-\\arcsin\\left(\\frac{4}{5}\\right)+2πn" } ], "meta": { "interimType": "Trig Apply Inverse Props 0Eq" } }, { "type": "interim", "title": "Solve $$20t-\\frac{π}{6}=\\arcsin\\left(\\frac{4}{5}\\right)+2πn:{\\quad}t=\\frac{πn}{10}+\\frac{π}{120}+\\frac{\\arcsin\\left(\\frac{4}{5}\\right)}{20}$$", "input": "20t-\\frac{π}{6}=\\arcsin\\left(\\frac{4}{5}\\right)+2πn", "steps": [ { "type": "interim", "title": "Move $$\\frac{π}{6}\\:$$to the right side", "input": "20t-\\frac{π}{6}=\\arcsin\\left(\\frac{4}{5}\\right)+2πn", "result": "20t=\\arcsin\\left(\\frac{4}{5}\\right)+2πn+\\frac{π}{6}", "steps": [ { "type": "step", "primary": "Add $$\\frac{π}{6}$$ to both sides", "result": "20t-\\frac{π}{6}+\\frac{π}{6}=\\arcsin\\left(\\frac{4}{5}\\right)+2πn+\\frac{π}{6}" }, { "type": "step", "primary": "Simplify", "result": "20t=\\arcsin\\left(\\frac{4}{5}\\right)+2πn+\\frac{π}{6}" } ], "meta": { "interimType": "Move to the Right Title 1Eq", "gptData": "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" } }, { "type": "interim", "title": "Divide both sides by $$20$$", "input": "20t=\\arcsin\\left(\\frac{4}{5}\\right)+2πn+\\frac{π}{6}", "result": "t=\\frac{πn}{10}+\\frac{π}{120}+\\frac{\\arcsin\\left(\\frac{4}{5}\\right)}{20}", "steps": [ { "type": "step", "primary": "Divide both sides by $$20$$", "result": "\\frac{20t}{20}=\\frac{\\arcsin\\left(\\frac{4}{5}\\right)}{20}+\\frac{2πn}{20}+\\frac{\\frac{π}{6}}{20}" }, { "type": "interim", "title": "Simplify", "input": "\\frac{20t}{20}=\\frac{\\arcsin\\left(\\frac{4}{5}\\right)}{20}+\\frac{2πn}{20}+\\frac{\\frac{π}{6}}{20}", "result": "t=\\frac{πn}{10}+\\frac{π}{120}+\\frac{\\arcsin\\left(\\frac{4}{5}\\right)}{20}", "steps": [ { "type": "interim", "title": "Simplify $$\\frac{20t}{20}:{\\quad}t$$", "input": "\\frac{20t}{20}", "steps": [ { "type": "step", "primary": "Divide the numbers: $$\\frac{20}{20}=1$$", "result": "=t" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7N/vk9x9k2kxWbnBd39r8GnyRHuGw7+tM5METTDj6vVHgWIADOS+aC1pY3tecNFb1ZEt3ZXAiqUE0HIXrrrezJHZKl2mV4AlztiApTAFigz3CTlQmE1/fQheZpbnqF2WqialcV/dI5TH4fXyp+ncwuA==" } }, { "type": "interim", "title": "Simplify $$\\frac{\\arcsin\\left(\\frac{4}{5}\\right)}{20}+\\frac{2πn}{20}+\\frac{\\frac{π}{6}}{20}:{\\quad}\\frac{πn}{10}+\\frac{π}{120}+\\frac{\\arcsin\\left(\\frac{4}{5}\\right)}{20}$$", "input": "\\frac{\\arcsin\\left(\\frac{4}{5}\\right)}{20}+\\frac{2πn}{20}+\\frac{\\frac{π}{6}}{20}", "steps": [ { "type": "step", "primary": "Group like terms", "result": "=\\frac{2πn}{20}+\\frac{\\frac{π}{6}}{20}+\\frac{\\arcsin\\left(\\frac{4}{5}\\right)}{20}" }, { "type": "interim", "title": "$$\\frac{2πn}{20}=\\frac{πn}{10}$$", "input": "\\frac{2πn}{20}", "steps": [ { "type": "step", "primary": "Cancel the common factor: $$2$$", "result": "=\\frac{πn}{10}" } ], "meta": { "solvingClass": "Solver", "interimType": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7YVyjdFRW0jf8Bxzp61JzqKDkfKJxJZVCmfBUAvjyrEn9ovYKijQYhJDCbxu/nAOJiNeObNakDzsmIPCImoPXKKN6Hv6MoTMtvtU0IQwXdn86gdrgplDSpsWofLl+kdTGUqU434AXMWrBF15m2LK04CS3daIZHtloJpe/PvtsyNI=" } }, { "type": "interim", "title": "$$\\frac{\\frac{π}{6}}{20}=\\frac{π}{120}$$", "input": "\\frac{\\frac{π}{6}}{20}", "steps": [ { "type": "step", "primary": "Apply the fraction rule: $$\\frac{\\frac{b}{c}}{a}=\\frac{b}{c\\:\\cdot\\:a}$$", "result": "=\\frac{π}{6\\cdot\\:20}" }, { "type": "step", "primary": "Multiply the numbers: $$6\\cdot\\:20=120$$", "result": "=\\frac{π}{120}" } ], "meta": { "solvingClass": "Solver", "interimType": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7tiTmKkmeEqHWILbBb88ajZJwMIjsqOGly4U/Md+VMz3dd47a0hQ8flDbGsI5To1d+bRvmdH+XexJq0YRmlk3dies2eVsPYBtJWOy7Dj5vAwjigtccxNWJk7pEnO8OW1UZYw0MdlPOPl7MbsS6qGyhrP9c7wanjYAh3/joXV85ZiwiNrEngO+NNvZ9sqNu+2V" } }, { "type": "step", "result": "=\\frac{πn}{10}+\\frac{π}{120}+\\frac{\\arcsin\\left(\\frac{4}{5}\\right)}{20}" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7x8E1LpWy1G5nlOFexfEIv2lkUkgP8w/RfbWyMvLLdcpVa09pOH/KPTJTG68euVJqs4UXzKL4ntNhP7qkM4/nKInF3R3Mi5YK7nnL155PpFAtOtZYwUjyXhDTsNnn6ElrSGpx9e3Lolh3WlYiBDdmOCdQBocAy6k+l2RX/XF+W6ROFQF+Syy7eTQaaWJetPHtMgiCEpcRtMUpkgCSytkbddc24FvZlNZ58BhvJmfcC56jeh7+jKEzLb7VNCEMF3Z/bMzoTd+5nEXVeQoBhpFcIKR8EHB59tBJBQA9xuadL8pRCyU/kC++nIKzwJ3x/l3dhf9RpaOf2FEQcHtD9y28DM6ZI3maOd47oU7wfog7YUqmtv/cETln0J5GtJo8PX+AJLd1ohke2Wgml78++2zI0g==" } }, { "type": "step", "result": "t=\\frac{πn}{10}+\\frac{π}{120}+\\frac{\\arcsin\\left(\\frac{4}{5}\\right)}{20}" } ], "meta": { "interimType": "Generic Simplify 0Eq" } } ], "meta": { "interimType": "Divide Both Sides Specific 1Eq", "gptData": 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$$20t-\\frac{π}{6}=π-\\arcsin\\left(\\frac{4}{5}\\right)+2πn:{\\quad}t=\\frac{π}{20}+\\frac{π}{120}+\\frac{πn}{10}-\\frac{\\arcsin\\left(\\frac{4}{5}\\right)}{20}$$", "input": "20t-\\frac{π}{6}=π-\\arcsin\\left(\\frac{4}{5}\\right)+2πn", "steps": [ { "type": "interim", "title": "Move $$\\frac{π}{6}\\:$$to the right side", "input": "20t-\\frac{π}{6}=π-\\arcsin\\left(\\frac{4}{5}\\right)+2πn", "result": "20t=π-\\arcsin\\left(\\frac{4}{5}\\right)+2πn+\\frac{π}{6}", "steps": [ { "type": "step", "primary": "Add $$\\frac{π}{6}$$ to both sides", "result": "20t-\\frac{π}{6}+\\frac{π}{6}=π-\\arcsin\\left(\\frac{4}{5}\\right)+2πn+\\frac{π}{6}" }, { "type": "step", "primary": "Simplify", "result": "20t=π-\\arcsin\\left(\\frac{4}{5}\\right)+2πn+\\frac{π}{6}" } ], "meta": { "interimType": "Move to the Right Title 1Eq", "gptData": "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" } }, { "type": "interim", "title": "Divide both sides by $$20$$", "input": "20t=π-\\arcsin\\left(\\frac{4}{5}\\right)+2πn+\\frac{π}{6}", "result": "t=\\frac{π}{20}+\\frac{π}{120}+\\frac{πn}{10}-\\frac{\\arcsin\\left(\\frac{4}{5}\\right)}{20}", "steps": [ { "type": "step", "primary": "Divide both sides by $$20$$", "result": "\\frac{20t}{20}=\\frac{π}{20}-\\frac{\\arcsin\\left(\\frac{4}{5}\\right)}{20}+\\frac{2πn}{20}+\\frac{\\frac{π}{6}}{20}" }, { "type": "interim", "title": "Simplify", "input": "\\frac{20t}{20}=\\frac{π}{20}-\\frac{\\arcsin\\left(\\frac{4}{5}\\right)}{20}+\\frac{2πn}{20}+\\frac{\\frac{π}{6}}{20}", "result": "t=\\frac{π}{20}+\\frac{π}{120}+\\frac{πn}{10}-\\frac{\\arcsin\\left(\\frac{4}{5}\\right)}{20}", "steps": [ { "type": "interim", "title": "Simplify $$\\frac{20t}{20}:{\\quad}t$$", "input": "\\frac{20t}{20}", "steps": [ { "type": "step", "primary": "Divide the numbers: $$\\frac{20}{20}=1$$", "result": "=t" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7N/vk9x9k2kxWbnBd39r8GnyRHuGw7+tM5METTDj6vVHgWIADOS+aC1pY3tecNFb1ZEt3ZXAiqUE0HIXrrrezJHZKl2mV4AlztiApTAFigz3CTlQmE1/fQheZpbnqF2WqialcV/dI5TH4fXyp+ncwuA==" } }, { "type": "interim", "title": "Simplify $$\\frac{π}{20}-\\frac{\\arcsin\\left(\\frac{4}{5}\\right)}{20}+\\frac{2πn}{20}+\\frac{\\frac{π}{6}}{20}:{\\quad}\\frac{π}{20}+\\frac{π}{120}+\\frac{πn}{10}-\\frac{\\arcsin\\left(\\frac{4}{5}\\right)}{20}$$", "input": "\\frac{π}{20}-\\frac{\\arcsin\\left(\\frac{4}{5}\\right)}{20}+\\frac{2πn}{20}+\\frac{\\frac{π}{6}}{20}", "steps": [ { "type": "step", "primary": "Group like terms", "result": "=\\frac{π}{20}+\\frac{2πn}{20}+\\frac{\\frac{π}{6}}{20}-\\frac{\\arcsin\\left(\\frac{4}{5}\\right)}{20}" }, { "type": "interim", "title": "$$\\frac{2πn}{20}=\\frac{πn}{10}$$", "input": "\\frac{2πn}{20}", "steps": [ { "type": "step", "primary": "Cancel the common factor: $$2$$", "result": "=\\frac{πn}{10}" } ], "meta": { "solvingClass": "Solver", "interimType": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7YVyjdFRW0jf8Bxzp61JzqKDkfKJxJZVCmfBUAvjyrEn9ovYKijQYhJDCbxu/nAOJiNeObNakDzsmIPCImoPXKKN6Hv6MoTMtvtU0IQwXdn86gdrgplDSpsWofLl+kdTGUqU434AXMWrBF15m2LK04CS3daIZHtloJpe/PvtsyNI=" } }, { "type": "interim", "title": "$$\\frac{\\frac{π}{6}}{20}=\\frac{π}{120}$$", "input": "\\frac{\\frac{π}{6}}{20}", "steps": [ { "type": "step", "primary": "Apply the fraction rule: $$\\frac{\\frac{b}{c}}{a}=\\frac{b}{c\\:\\cdot\\:a}$$", "result": "=\\frac{π}{6\\cdot\\:20}" }, { "type": "step", "primary": "Multiply the numbers: $$6\\cdot\\:20=120$$", "result": "=\\frac{π}{120}" } ], "meta": { "solvingClass": "Solver", "interimType": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7tiTmKkmeEqHWILbBb88ajZJwMIjsqOGly4U/Md+VMz3dd47a0hQ8flDbGsI5To1d+bRvmdH+XexJq0YRmlk3dies2eVsPYBtJWOy7Dj5vAwjigtccxNWJk7pEnO8OW1UZYw0MdlPOPl7MbsS6qGyhrP9c7wanjYAh3/joXV85ZiwiNrEngO+NNvZ9sqNu+2V" } }, { "type": "step", "result": "=\\frac{π}{20}+\\frac{πn}{10}+\\frac{π}{120}-\\frac{\\arcsin\\left(\\frac{4}{5}\\right)}{20}" }, { "type": "step", "primary": "Group like terms", "result": "=\\frac{π}{20}+\\frac{π}{120}+\\frac{πn}{10}-\\frac{\\arcsin\\left(\\frac{4}{5}\\right)}{20}" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7DBVukKVLyeXzzJv74F9Zi+SdWCuzhK/yYl9fD/foektRCyU/kC++nIKzwJ3x/l3dhf9RpaOf2FEQcHtD9y28DM6ZI3maOd47oU7wfog7YUqwHg6EygcbX8SZRbOywcSnVdNK6b/PmQukzNdLVQkh7NMQ0vmOWo9IZfhei7w2gJaOcT8EoaLBL67N6Af98Q+baHt1BgzBw5/O+Topa8ZRccE37CuTdlgbpSNwk/jdpFBvY2vln5EVCgXaTgt0uv5N62afPPKeAkD+SYP68dk3Ce9sGZu5A1MXROmEpnxG69ryk4whNiKT03wC0hzj1bDV/g2kW+kVRtPOaoZaey2mO0yP/+rp8WOb1jdy0EtBd59sIF6dfn90WdxznxKCAr1Qna97GSU5e2vf0Alk9Y6qjOGfi/MUDlnzaRn5AhKrKO1YBBKEr4xcqy+XQzs9kshb" } }, { "type": "step", "result": "t=\\frac{π}{20}+\\frac{π}{120}+\\frac{πn}{10}-\\frac{\\arcsin\\left(\\frac{4}{5}\\right)}{20}" } ], "meta": { "interimType": "Generic Simplify 0Eq" } } ], "meta": { "interimType": "Divide Both Sides Specific 1Eq", "gptData": 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"t=\\frac{πn}{10}+\\frac{π}{120}+\\frac{\\arcsin\\left(\\frac{4}{5}\\right)}{20},\\:t=\\frac{π}{20}+\\frac{π}{120}+\\frac{πn}{10}-\\frac{\\arcsin\\left(\\frac{4}{5}\\right)}{20}" }, { "type": "step", "primary": "Show solutions in decimal form", "result": "t=\\frac{πn}{10}+\\frac{π}{120}+\\frac{0.92729…}{20},\\:t=\\frac{π}{20}+\\frac{π}{120}+\\frac{πn}{10}-\\frac{0.92729…}{20}" } ], "meta": { "solvingClass": "Trig Equations", "practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Trig%20Equations", "practiceTopic": "Trig Equations" } }, "plot_output": { "meta": { "plotInfo": { "variable": "t", "plotRequest": "10\\sin(20t-\\frac{π}{6})-8" }, "showViewLarger": true } }, "meta": { "showVerify": true } }