35.35=100cos(x)

{ "query": { "display": "$$35.35=100\\cos\\left(x\\right)$$", "symbolab_question": "EQUATION#35.35=100\\cos(x)" }, "solution": { "level": "PERFORMED", "subject": "Trigonometry", "topic": "Trig Equations", "subTopic": "Trig Equations", "default": "x=1.20948…+2πn,x=2π-1.20948…+2πn", "degrees": "x=69.29845…^{\\circ }+360^{\\circ }n,x=290.70154…^{\\circ }+360^{\\circ }n", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$35.35=100\\cos\\left(x\\right){\\quad:\\quad}x=1.20948…+2πn,\\:x=2π-1.20948…+2πn$$", "input": "35.35=100\\cos\\left(x\\right)", "steps": [ { "type": "step", "primary": "Switch sides", "result": "100\\cos\\left(x\\right)=35.35" }, { "type": "interim", "title": "Divide both sides by $$100$$", "input": "100\\cos\\left(x\\right)=35.35", "result": "\\cos\\left(x\\right)=0.3535", "steps": [ { "type": "step", "primary": "Divide both sides by $$100$$", "result": "\\frac{100\\cos\\left(x\\right)}{100}=\\frac{35.35}{100}" }, { "type": "step", "primary": "Simplify", "result": "\\cos\\left(x\\right)=0.3535" } ], "meta": { "interimType": "Divide Both Sides Specific 1Eq", "gptData": "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" } }, { "type": "interim", "title": "Apply trig inverse properties", "input": "\\cos\\left(x\\right)=0.3535", "result": "x=\\arccos\\left(0.3535\\right)+2πn,\\:x=2π-\\arccos\\left(0.3535\\right)+2πn", "steps": [ { "type": "step", "primary": "General solutions for $$\\cos\\left(x\\right)=0.3535$$", "secondary": [ "$$\\cos\\left(x\\right)=a\\quad\\Rightarrow\\quad\\:x=\\arccos\\left(a\\right)+2πn,\\:\\quad\\:x=2π-\\arccos\\left(a\\right)+2πn$$" ], "result": "x=\\arccos\\left(0.3535\\right)+2πn,\\:x=2π-\\arccos\\left(0.3535\\right)+2πn" } ], "meta": { "interimType": "Trig Apply Inverse Props 0Eq" } }, { "type": "step", "primary": "Show solutions in decimal form", "result": "x=1.20948…+2πn,\\:x=2π-1.20948…+2πn" } ], "meta": { "solvingClass": "Trig Equations", "practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Trig%20Equations", "practiceTopic": "Trig Equations" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "35.35-100\\cos(x)" }, "showViewLarger": true } }, "meta": { "showVerify": true } }