tan(2θ)=0.55

{ "query": { "display": "$$\\tan\\left(2θ\\right)=0.55$$", "symbolab_question": "EQUATION#\\tan(2θ)=0.55" }, "solution": { "level": "PERFORMED", "subject": "Trigonometry", "topic": "Trig Equations", "subTopic": "Trig Equations", "default": "θ=\\frac{0.50284…}{2}+\\frac{πn}{2}", "degrees": "θ=14.40539…^{\\circ }+90^{\\circ }n", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\tan\\left(2θ\\right)=0.55{\\quad:\\quad}θ=\\frac{0.50284…}{2}+\\frac{πn}{2}$$", "input": "\\tan\\left(2θ\\right)=0.55", "steps": [ { "type": "interim", "title": "Apply trig inverse properties", "input": "\\tan\\left(2θ\\right)=0.55", "result": "2θ=\\arctan\\left(0.55\\right)+πn", "steps": [ { "type": "step", "primary": "General solutions for $$\\tan\\left(2θ\\right)=0.55$$", "secondary": [ "$$\\tan\\left(x\\right)=a\\quad\\Rightarrow\\quad\\:x=\\arctan\\left(a\\right)+πn$$" ], "result": "2θ=\\arctan\\left(0.55\\right)+πn" } ], "meta": { "interimType": "Trig Apply Inverse Props 0Eq" } }, { "type": "interim", "title": "Solve $$2θ=\\arctan\\left(0.55\\right)+πn:{\\quad}θ=\\frac{\\arctan\\left(0.55\\right)}{2}+\\frac{πn}{2}$$", "input": "2θ=\\arctan\\left(0.55\\right)+πn", "steps": [ { "type": "interim", "title": "Divide both sides by $$2$$", "input": "2θ=\\arctan\\left(0.55\\right)+πn", "result": "θ=\\frac{\\arctan\\left(0.55\\right)}{2}+\\frac{πn}{2}", "steps": [ { "type": "step", "primary": "Divide both sides by $$2$$", "result": "\\frac{2θ}{2}=\\frac{\\arctan\\left(0.55\\right)}{2}+\\frac{πn}{2}" }, { "type": "step", "primary": "Simplify", "result": "θ=\\frac{\\arctan\\left(0.55\\right)}{2}+\\frac{πn}{2}" } ], "meta": { "interimType": "Divide Both Sides Specific 1Eq", "gptData": "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" } } ], "meta": { "solvingClass": "Equations", "interimType": "Generic Solve Title 1Eq" } }, { "type": "step", "result": "θ=\\frac{\\arctan\\left(0.55\\right)}{2}+\\frac{πn}{2}" }, { "type": "step", "primary": "Show solutions in decimal form", "result": "θ=\\frac{0.50284…}{2}+\\frac{πn}{2}" } ], "meta": { "solvingClass": "Trig Equations", "practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Trig%20Equations", "practiceTopic": "Trig Equations" } }, "plot_output": { "meta": { "plotInfo": { "variable": "θ", "plotRequest": "\\tan(2θ)-0.55" }, "showViewLarger": true } }, "meta": { "showVerify": true } }