solvefor θ,x=2sec(θ)

{ "query": { "display": "solve for $$θ,\\:x=2\\sec\\left(θ\\right)$$", "symbolab_question": "SOLVE_FOR#solvefor θ,x=2\\sec(θ)" }, "solution": { "level": "PERFORMED", "subject": "Trigonometry", "topic": "Trig Equations", "subTopic": "Trig Equations", "default": "θ=\\arcsec(\\frac{x}{2})+2πn,θ=-\\arcsec(\\frac{x}{2})+2πn", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$solve\\:for\\:θ,\\:x=2\\sec\\left(θ\\right){\\quad:\\quad}θ=\\arcsec\\left(\\frac{x}{2}\\right)+2πn,\\:θ=-\\arcsec\\left(\\frac{x}{2}\\right)+2πn$$", "input": "x=2\\sec\\left(θ\\right)", "steps": [ { "type": "step", "primary": "Switch sides", "result": "2\\sec\\left(θ\\right)=x" }, { "type": "interim", "title": "Divide both sides by $$2$$", "input": "2\\sec\\left(θ\\right)=x", "result": "\\sec\\left(θ\\right)=\\frac{x}{2}", "steps": [ { "type": "step", "primary": "Divide both sides by $$2$$", "result": "\\frac{2\\sec\\left(θ\\right)}{2}=\\frac{x}{2}" }, { "type": "step", "primary": "Simplify", "result": "\\sec\\left(θ\\right)=\\frac{x}{2}" } ], "meta": { "interimType": "Divide Both Sides Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7xqDNX42OyJjPevbF+7IBnjTxds+Nrjg+AIXFqVTQSKvVh90DS7J9J40zZjnm5cN365VeVDIdizrNAR8IgglmA/dXUPMskG7qiavExrN923MX1edlCI54zkb+umgtj3TNCgP2aTmf+vckfrbkp+gYGdIWMxer8Y0maDEiJwmPzz0Gzvef9somTq4fFXcfzhz7pFrLbja3ehyVzzvKAKafI4ze3n+NJGQTzJSZEjOiRy+n6WU7ybUlSwezFhLKvkKNVvuqUoYkKmBK6fSR2cNlgkfqfT3HSxldmNt6rUcfvySCyrAO9zMQDZyjEiWM7qI5HNLamESyiXkEVNU4Be3yXlX3rP7J381OCLdf7C7WWRDvbBmbuQNTF0TphKZ8RuvaTbBiSexc/wbzzjAmcOEO4Hl9dYdOWW7s8LScShR+x1w=" } }, { "type": "interim", "title": "Apply trig inverse properties", "input": "\\sec\\left(θ\\right)=\\frac{x}{2}", "result": "θ=\\arcsec\\left(\\frac{x}{2}\\right)+2πn,\\:θ=-\\arcsec\\left(\\frac{x}{2}\\right)+2πn", "steps": [ { "type": "step", "primary": "General solutions for $$\\sec\\left(θ\\right)=\\frac{x}{2}$$", "secondary": [ "$$\\sec\\left(x\\right)=a\\quad\\Rightarrow\\quad\\:x=\\arcsec\\left(a\\right)+2πn,\\:\\quad\\:x=-\\arcsec\\left(a\\right)+2πn$$" ], "result": "θ=\\arcsec\\left(\\frac{x}{2}\\right)+2πn,\\:θ=-\\arcsec\\left(\\frac{x}{2}\\right)+2πn" } ], "meta": { "interimType": "Trig Apply Inverse Props 0Eq" } } ], "meta": { "solvingClass": "Trig Equations", "practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Trig%20Equations", "practiceTopic": "Trig Equations" } }, "plot_output": { "meta": { "plotInfo": { "variable": "θ", "plotRequest": "x-2\\sec(θ)" }, "showViewLarger": true } }, "meta": { "showVerify": true } }