{ "query": { "display": "solve for $$θ,\\:\\cot\\left(θ\\right)=-\\frac{π}{6}$$", "symbolab_question": "SOLVE_FOR#solvefor θ,\\cot(θ)=-\\frac{π}{6}" }, "solution": { "level": "PERFORMED", "subject": "Trigonometry", "topic": "Trig Equations", "subTopic": "Trig Equations", "default": "θ=2.05314…+πn", "degrees": "θ=117.63649…^{\\circ }+180^{\\circ }n", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$solve\\:for\\:θ,\\:\\cot\\left(θ\\right)=-\\frac{π}{6}{\\quad:\\quad}θ=2.05314…+πn$$", "input": "\\cot\\left(θ\\right)=-\\frac{π}{6}", "steps": [ { "type": "interim", "title": "Apply trig inverse properties", "input": "\\cot\\left(θ\\right)=-\\frac{π}{6}", "result": "θ=\\arccot\\left(-\\frac{π}{6}\\right)+πn", "steps": [ { "type": "step", "primary": "General solutions for $$\\cot\\left(θ\\right)=-\\frac{π}{6}$$", "secondary": [ "$$\\cot\\left(x\\right)=-a\\quad\\Rightarrow\\quad\\:x=\\arccot\\left(-a\\right)+πn$$" ], "result": "θ=\\arccot\\left(-\\frac{π}{6}\\right)+πn" } ], "meta": { "interimType": "Trig Apply Inverse Props 0Eq" } }, { "type": "step", "primary": "Show solutions in decimal form", "result": "θ=2.05314…+πn" } ], "meta": { "solvingClass": "Trig Equations", "practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Trig%20Equations", "practiceTopic": "Trig Equations" } }, "plot_output": { "meta": { "plotInfo": { "variable": "θ", "plotRequest": "\\cot(θ)+\\frac{π}{6}" }, "showViewLarger": true } }, "meta": { "showVerify": true } }