(3sqrt(3))/(14)=sin(x)

{ "query": { "display": "$$\\frac{3\\sqrt{3}}{14}=\\sin\\left(x\\right)$$", "symbolab_question": "EQUATION#\\frac{3\\sqrt{3}}{14}=\\sin(x)" }, "solution": { "level": "PERFORMED", "subject": "Trigonometry", "topic": "Trig Equations", "subTopic": "Trig Equations", "default": "x=0.38025…+2πn,x=π-0.38025…+2πn", "degrees": "x=21.78678…^{\\circ }+360^{\\circ }n,x=158.21321…^{\\circ }+360^{\\circ }n", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\frac{3\\sqrt{3}}{14}=\\sin\\left(x\\right){\\quad:\\quad}x=0.38025…+2πn,\\:x=π-0.38025…+2πn$$", "input": "\\frac{3\\sqrt{3}}{14}=\\sin\\left(x\\right)", "steps": [ { "type": "step", "primary": "Switch sides", "result": "\\sin\\left(x\\right)=\\frac{3\\sqrt{3}}{14}" }, { "type": "interim", "title": "Apply trig inverse properties", "input": "\\sin\\left(x\\right)=\\frac{3\\sqrt{3}}{14}", "result": "x=\\arcsin\\left(\\frac{3\\sqrt{3}}{14}\\right)+2πn,\\:x=π-\\arcsin\\left(\\frac{3\\sqrt{3}}{14}\\right)+2πn", "steps": [ { "type": "step", "primary": "General solutions for $$\\sin\\left(x\\right)=\\frac{3\\sqrt{3}}{14}$$", "secondary": [ "$$\\sin\\left(x\\right)=a\\quad\\Rightarrow\\quad\\:x=\\arcsin\\left(a\\right)+2πn,\\:\\quad\\:x=π-\\arcsin\\left(a\\right)+2πn$$" ], "result": "x=\\arcsin\\left(\\frac{3\\sqrt{3}}{14}\\right)+2πn,\\:x=π-\\arcsin\\left(\\frac{3\\sqrt{3}}{14}\\right)+2πn" } ], "meta": { "interimType": "Trig Apply Inverse Props 0Eq" } }, { "type": "step", "primary": "Show solutions in decimal form", "result": "x=0.38025…+2πn,\\:x=π-0.38025…+2πn" } ], "meta": { "solvingClass": "Trig Equations", "practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Trig%20Equations", "practiceTopic": "Trig Equations" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "\\frac{3\\sqrt{3}}{14}-\\sin(x)" }, "showViewLarger": true } }, "meta": { "showVerify": true } }