3arcsin(2θ)=2pi

{ "query": { "display": "$$3\\arcsin\\left(2θ\\right)=2π$$", "symbolab_question": "EQUATION#3\\arcsin(2θ)=2π" }, "solution": { "level": "PERFORMED", "subject": "Trigonometry", "topic": "Trig Equations", "subTopic": "Trig Equations", "default": "\\mathrm{No\\:Solution\\:for}\\:θ\\in\\mathbb{R}", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$3\\arcsin\\left(2θ\\right)=2π{\\quad:\\quad}$$No Solution for $$θ\\in\\mathbb{R}$$", "input": "3\\arcsin\\left(2θ\\right)=2π", "steps": [ { "type": "interim", "title": "Divide both sides by $$3$$", "input": "3\\arcsin\\left(2θ\\right)=2π", "result": "\\arcsin\\left(2θ\\right)=\\frac{2π}{3}", "steps": [ { "type": "step", "primary": "Divide both sides by $$3$$", "result": "\\frac{3\\arcsin\\left(2θ\\right)}{3}=\\frac{2π}{3}" }, { "type": "step", "primary": "Simplify", "result": "\\arcsin\\left(2θ\\right)=\\frac{2π}{3}" } ], "meta": { "interimType": "Divide Both Sides Specific 1Eq", "gptData": "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" } }, { "type": "step", "primary": "$$-\\frac{\\pi}{2}\\le\\arcsin\\left(x\\right)\\le\\frac{\\pi}{2}$$", "result": "\\mathrm{No\\:Solution\\:for}\\:θ\\in\\mathbb{R}" } ], "meta": { "solvingClass": "Trig Equations", "practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Trig%20Equations", "practiceTopic": "Trig Equations" } }, "plot_output": { "meta": { "plotInfo": { "variable": "θ", "plotRequest": "3\\arcsin(2θ)-2π" }, "showViewLarger": true } }, "meta": { "showVerify": true } }