4-2sin(x)=0

{ "query": { "display": "$$4-2\\sin\\left(x\\right)=0$$", "symbolab_question": "EQUATION#4-2\\sin(x)=0" }, "solution": { "level": "PERFORMED", "subject": "Trigonometry", "topic": "Trig Equations", "subTopic": "Trig Equations", "default": "\\mathrm{No\\:Solution\\:for}\\:x\\in\\mathbb{R}", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$4-2\\sin\\left(x\\right)=0{\\quad:\\quad}$$No Solution for $$x\\in\\mathbb{R}$$", "input": "4-2\\sin\\left(x\\right)=0", "steps": [ { "type": "interim", "title": "Move $$4\\:$$to the right side", "input": "4-2\\sin\\left(x\\right)=0", "result": "-2\\sin\\left(x\\right)=-4", "steps": [ { "type": "step", "primary": "Subtract $$4$$ from both sides", "result": "4-2\\sin\\left(x\\right)-4=0-4" }, { "type": "step", "primary": "Simplify", "result": "-2\\sin\\left(x\\right)=-4" } ], "meta": { "interimType": "Move to the Right Title 1Eq", "gptData": "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" } }, { "type": "interim", "title": "Divide both sides by $$-2$$", "input": "-2\\sin\\left(x\\right)=-4", "result": "\\sin\\left(x\\right)=2", "steps": [ { "type": "step", "primary": "Divide both sides by $$-2$$", "result": "\\frac{-2\\sin\\left(x\\right)}{-2}=\\frac{-4}{-2}" }, { "type": "interim", "title": "Simplify", "input": "\\frac{-2\\sin\\left(x\\right)}{-2}=\\frac{-4}{-2}", "result": "\\sin\\left(x\\right)=2", "steps": [ { "type": "interim", "title": "Simplify $$\\frac{-2\\sin\\left(x\\right)}{-2}:{\\quad}\\sin\\left(x\\right)$$", "input": "\\frac{-2\\sin\\left(x\\right)}{-2}", "steps": [ { "type": "step", "primary": "Apply the fraction rule: $$\\frac{-a}{-b}=\\frac{a}{b}$$", "result": "=\\frac{2\\sin\\left(x\\right)}{2}" }, { "type": "step", "primary": "Divide the numbers: $$\\frac{2}{2}=1$$", "result": "=\\sin\\left(x\\right)" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7ykK5tHgflMg5Gr7e5mFlqEmKh9SD8Q7TZ4UQ7A4hUAl1g99dC9fj9sg0EHzBIRDRbNn5zlmPNcA5aps+SmEVLEUqTd96MWTKI6Kr2Ib0iQAi5KYlQO0vFE/Inns2Sruq5DLz90sj0YHthJBpFJezVbaWmezUas9sj/VsI6hQc9E=" } }, { "type": "interim", "title": "Simplify $$\\frac{-4}{-2}:{\\quad}2$$", "input": "\\frac{-4}{-2}", "steps": [ { "type": "step", "primary": "Apply the fraction rule: $$\\frac{-a}{-b}=\\frac{a}{b}$$", "result": "=\\frac{4}{2}" }, { "type": "step", "primary": "Divide the numbers: $$\\frac{4}{2}=2$$", "result": "=2" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7NVC5MCHOYbiDjGYE4ZqzZgCWKUbvV6WK3fDUgFtg3Q8kLk5B3NY35r4MgzhzVzFVo3oe/oyhMy2+1TQhDBd2f2zM6E3fuZxF1XkKAYaRXCDRYwlVz1ZOemykx7rrL7E8vzIPeEtDfcHv/z8uls8Teg==" } }, { "type": "step", "result": "\\sin\\left(x\\right)=2" } ], "meta": { "interimType": "Generic Simplify 0Eq" } } ], "meta": { "interimType": "Divide Both Sides Specific 1Eq", "gptData": "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" } }, { "type": "step", "primary": "$$-1\\le\\sin\\left(x\\right)\\le1$$", "result": "\\mathrm{No\\:Solution\\:for}\\:x\\in\\mathbb{R}" } ], "meta": { "solvingClass": "Trig Equations", "practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Trig%20Equations", "practiceTopic": "Trig Equations" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "4-2\\sin(x)" }, "showViewLarger": true } }, "meta": { "showVerify": true } }