{ "query": { "display": "$$\\tan\\left(x\\right)=\\frac{10}{18}$$", "symbolab_question": "EQUATION#\\tan(x)=\\frac{10}{18}" }, "solution": { "level": "PERFORMED", "subject": "Trigonometry", "topic": "Trig Equations", "subTopic": "Trig Equations", "default": "x=0.50709…+πn", "degrees": "x=29.05460…^{\\circ }+180^{\\circ }n", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\tan\\left(x\\right)=\\frac{10}{18}{\\quad:\\quad}x=0.50709…+πn$$", "input": "\\tan\\left(x\\right)=\\frac{10}{18}", "steps": [ { "type": "step", "primary": "Cancel the common factor: $$2$$", "result": "\\tan\\left(x\\right)=\\frac{5}{9}" }, { "type": "interim", "title": "Apply trig inverse properties", "input": "\\tan\\left(x\\right)=\\frac{5}{9}", "result": "x=\\arctan\\left(\\frac{5}{9}\\right)+πn", "steps": [ { "type": "step", "primary": "General solutions for $$\\tan\\left(x\\right)=\\frac{5}{9}$$", "secondary": [ "$$\\tan\\left(x\\right)=a\\quad\\Rightarrow\\quad\\:x=\\arctan\\left(a\\right)+πn$$" ], "result": "x=\\arctan\\left(\\frac{5}{9}\\right)+πn" } ], "meta": { "interimType": "Trig Apply Inverse Props 0Eq" } }, { "type": "step", "primary": "Show solutions in decimal form", "result": "x=0.50709…+πn" } ], "meta": { "solvingClass": "Trig Equations", "practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Trig%20Equations", "practiceTopic": "Trig Equations" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "\\tan(x)-\\frac{10}{18}" }, "showViewLarger": true } }, "meta": { "showVerify": true } }