1/(sin(30))

{ "query": { "display": "$$\\frac{1}{\\sin\\left(30^{\\circ\\:}\\right)}$$", "symbolab_question": "TRIG_EVALUATE#\\frac{1}{\\sin(30^{\\circ })}" }, "solution": { "level": "PERFORMED", "subject": "Trigonometry", "topic": "Evaluate Functions", "subTopic": "Simplified", "default": "2", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\frac{1}{\\sin\\left(30^{\\circ\\:}\\right)}=2$$", "input": "\\frac{1}{\\sin\\left(30^{\\circ\\:}\\right)}", "steps": [ { "type": "interim", "title": "Use the following trivial identity:$${\\quad}\\sin\\left(30^{\\circ\\:}\\right)=\\frac{1}{2}$$", "input": "\\sin\\left(30^{\\circ\\:}\\right)", "steps": [ { "type": "step", "primary": "$$\\sin\\left(x\\right)$$ periodicity table with $$360^{\\circ\\:}n$$ cycle:<br/>$$\\begin{array}{|c|c|c|c|}\\hline x&\\sin(x)&x&\\sin(x)\\\\\\hline 0&0&180^{\\circ }&0\\\\\\hline 30^{\\circ }&\\frac{1}{2}&210^{\\circ }&-\\frac{1}{2}\\\\\\hline 45^{\\circ }&\\frac{\\sqrt{2}}{2}&225^{\\circ }&-\\frac{\\sqrt{2}}{2}\\\\\\hline 60^{\\circ }&\\frac{\\sqrt{3}}{2}&240^{\\circ }&-\\frac{\\sqrt{3}}{2}\\\\\\hline 90^{\\circ }&1&270^{\\circ }&-1\\\\\\hline 120^{\\circ }&\\frac{\\sqrt{3}}{2}&300^{\\circ }&-\\frac{\\sqrt{3}}{2}\\\\\\hline 135^{\\circ }&\\frac{\\sqrt{2}}{2}&315^{\\circ }&-\\frac{\\sqrt{2}}{2}\\\\\\hline 150^{\\circ }&\\frac{1}{2}&330^{\\circ }&-\\frac{1}{2}\\\\\\hline \\end{array}$$" }, { "type": "step", "result": "=\\frac{1}{2}" } ], "meta": { "interimType": "Trig Trivial Angle Value Title 0Eq" } }, { "type": "step", "result": "=\\frac{1}{\\frac{1}{2}}" }, { "type": "step", "primary": "Simplify", "result": "=2" } ], "meta": { "solvingClass": "Trig Evaluate", "practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Evaluate%20Functions", "practiceTopic": "Evaluate Functions" } }, "meta": { "showVerify": true } }