(sin(x))/(25)=(sin(125))/(165.6)

{ "query": { "display": "$$\\frac{\\sin\\left(x\\right)}{25}=\\frac{\\sin\\left(125^{\\circ\\:}\\right)}{165.6}$$", "symbolab_question": "EQUATION#\\frac{\\sin(x)}{25}=\\frac{\\sin(125^{\\circ })}{165.6}" }, "solution": { "level": "PERFORMED", "subject": "Trigonometry", "topic": "Trig Equations", "subTopic": "Trig Equations", "default": "x=0.12398…+360^{\\circ }n,x=180^{\\circ }-0.12398…+360^{\\circ }n", "radians": "x=0.12398…+2πn,x=π-0.12398…+2πn", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\frac{\\sin\\left(x\\right)}{25}=\\frac{\\sin\\left(125^{\\circ\\:}\\right)}{165.6}{\\quad:\\quad}x=0.12398…+360^{\\circ\\:}n,\\:x=180^{\\circ\\:}-0.12398…+360^{\\circ\\:}n$$", "input": "\\frac{\\sin\\left(x\\right)}{25}=\\frac{\\sin\\left(125^{\\circ\\:}\\right)}{165.6}", "steps": [ { "type": "interim", "title": "Multiply both sides by $$25$$", "input": "\\frac{\\sin\\left(x\\right)}{25}=\\frac{\\sin\\left(125^{\\circ\\:}\\right)}{165.6}", "result": "\\sin\\left(x\\right)=\\frac{25\\sin\\left(125^{\\circ\\:}\\right)}{165.6}", "steps": [ { "type": "step", "primary": "Multiply both sides by $$25$$", "result": "\\frac{25\\sin\\left(x\\right)}{25}=\\frac{25\\sin\\left(125^{\\circ\\:}\\right)}{165.6}" }, { "type": "step", "primary": "Simplify", "result": "\\sin\\left(x\\right)=\\frac{25\\sin\\left(125^{\\circ\\:}\\right)}{165.6}" } ], "meta": { "interimType": "Multiply Both Sides Specific 1Eq", "gptData": "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" } }, { "type": "interim", "title": "Apply trig inverse properties", "input": "\\sin\\left(x\\right)=\\frac{25\\sin\\left(125^{\\circ\\:}\\right)}{165.6}", "result": "x=\\arcsin\\left(\\frac{25\\sin\\left(125^{\\circ\\:}\\right)}{165.6}\\right)+360^{\\circ\\:}n,\\:x=180^{\\circ\\:}-\\arcsin\\left(\\frac{25\\sin\\left(125^{\\circ\\:}\\right)}{165.6}\\right)+360^{\\circ\\:}n", "steps": [ { "type": "step", "primary": "General solutions for $$\\sin\\left(x\\right)=\\frac{25\\sin\\left(125^{\\circ\\:}\\right)}{165.6}$$", "secondary": [ "$$\\sin\\left(x\\right)=a\\quad\\Rightarrow\\quad\\:x=\\arcsin\\left(a\\right)+360^{\\circ\\:}n,\\:\\quad\\:x=180^{\\circ\\:}-\\arcsin\\left(a\\right)+360^{\\circ\\:}n$$" ], "result": "x=\\arcsin\\left(\\frac{25\\sin\\left(125^{\\circ\\:}\\right)}{165.6}\\right)+360^{\\circ\\:}n,\\:x=180^{\\circ\\:}-\\arcsin\\left(\\frac{25\\sin\\left(125^{\\circ\\:}\\right)}{165.6}\\right)+360^{\\circ\\:}n" } ], "meta": { "interimType": "Trig Apply Inverse Props 0Eq" } }, { "type": "step", "primary": "Show solutions in decimal form", "result": "x=0.12398…+360^{\\circ\\:}n,\\:x=180^{\\circ\\:}-0.12398…+360^{\\circ\\:}n" } ], "meta": { "solvingClass": "Trig Equations", "practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Trig%20Equations", "practiceTopic": "Trig Equations" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "\\frac{\\sin(x)}{25}-\\frac{\\sin(125^{\\circ })}{165.6}" }, "showViewLarger": true } }, "meta": { "showVerify": true } }