50*sin(30)

{ "query": { "display": "$$50\\cdot\\:\\sin\\left(30^{\\circ\\:}\\right)$$", "symbolab_question": "TRIG_EVALUATE#50\\cdot \\sin(30^{\\circ })" }, "solution": { "level": "PERFORMED", "subject": "Trigonometry", "topic": "Evaluate Functions", "subTopic": "Simplified", "default": "25", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$50\\sin\\left(30^{\\circ\\:}\\right)=25$$", "input": "50\\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": "=50\\cdot\\:\\frac{1}{2}" }, { "type": "interim", "title": "Simplify $$50\\cdot\\:\\frac{1}{2}:{\\quad}25$$", "input": "50\\cdot\\:\\frac{1}{2}", "result": "=25", "steps": [ { "type": "step", "primary": "Convert element to fraction: $$50=\\frac{50}{1}$$", "result": "=\\frac{1}{2}\\cdot\\:\\frac{50}{1}" }, { "type": "step", "primary": "Cross-cancel common factor: $$2$$", "result": "=\\frac{25}{1}" }, { "type": "step", "primary": "Apply the fraction rule: $$\\frac{a}{1}=a$$", "result": "=25" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7hdOTGGl7vmFfS6K9snTkzLCVpDAG11IdQLl4eKYIiFMJQJZuTAY5js+oqjdT8kslaL2+z2IkAduonrMCKN3WAR429vuTSxWa7B/X3D1oP03iMq6Avti/HzMXacfy1R4fQPpwPm1Z+hwEbINNneEzRyS3daIZHtloJpe/PvtsyNI=" } } ], "meta": { "solvingClass": "Trig Evaluate", "practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Evaluate%20Functions", "practiceTopic": "Evaluate Functions" } }, "meta": { "showVerify": true } }