tan(240)

{ "query": { "display": "$$\\tan\\left(240^{\\circ\\:}\\right)$$", "symbolab_question": "TRIG_EVALUATE#\\tan(240^{\\circ })" }, "solution": { "level": "PERFORMED", "subject": "Trigonometry", "topic": "Evaluate Functions", "subTopic": "Simplified", "default": "\\sqrt{3}", "decimal": "1.73205…", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\tan\\left(240^{\\circ\\:}\\right)=\\sqrt{3}$$", "input": "\\tan\\left(240^{\\circ\\:}\\right)", "steps": [ { "type": "interim", "title": "$$\\tan\\left(240^{\\circ\\:}\\right)=\\tan\\left(60^{\\circ\\:}\\right)$$", "input": "\\tan\\left(240^{\\circ\\:}\\right)", "result": "=\\tan\\left(60^{\\circ\\:}\\right)", "steps": [ { "type": "step", "primary": "Rewrite $$240^{\\circ\\:}$$ as $$180^{\\circ\\:}+60^{\\circ\\:}$$", "result": "=\\tan\\left(180^{\\circ\\:}+60^{\\circ\\:}\\right)" }, { "type": "step", "primary": "Apply the periodicity of $$\\tan$$: $$\\tan\\left(x+180^{\\circ\\:}\\right)=\\tan\\left(x\\right)$$", "secondary": [ "$$\\tan\\left(180^{\\circ\\:}+60^{\\circ\\:}\\right)=\\tan\\left(60^{\\circ\\:}\\right)$$" ], "result": "=\\tan\\left(60^{\\circ\\:}\\right)" } ], "meta": { "interimType": "N/A" } }, { "type": "interim", "title": "Use the following trivial identity:$${\\quad}\\tan\\left(60^{\\circ\\:}\\right)=\\sqrt{3}$$", "input": "\\tan\\left(60^{\\circ\\:}\\right)", "steps": [ { "type": "step", "primary": "$$\\tan\\left(x\\right)$$ periodicity table with $$180^{\\circ\\:}n$$ cycle:<br/>$$\\begin{array}{|c|c|}\\hline x&\\tan(x)\\\\\\hline 0&0\\\\\\hline 30^{\\circ }&\\frac{\\sqrt{3}}{3}\\\\\\hline 45^{\\circ }&1\\\\\\hline 60^{\\circ }&\\sqrt{3}\\\\\\hline 90^{\\circ }&\\pm\\infty\\\\\\hline 120^{\\circ }&-\\sqrt{3}\\\\\\hline 135^{\\circ }&-1\\\\\\hline 150^{\\circ }&-\\frac{\\sqrt{3}}{3}\\\\\\hline &\\\\\\hline \\end{array}$$" }, { "type": "step", "result": "=\\sqrt{3}" } ], "meta": { "interimType": "Trig Trivial Angle Value Title 0Eq" } }, { "type": "step", "result": "=\\sqrt{3}" } ], "meta": { "solvingClass": "Trig Evaluate", "practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Evaluate%20Functions", "practiceTopic": "Evaluate Functions" } }, "meta": { "showVerify": true } }