30*sin(45)

{ "query": { "display": "$$30\\cdot\\:\\sin\\left(45^{\\circ\\:}\\right)$$", "symbolab_question": "TRIG_EVALUATE#30\\cdot \\sin(45^{\\circ })" }, "solution": { "level": "PERFORMED", "subject": "Trigonometry", "topic": "Evaluate Functions", "subTopic": "Simplified", "default": "15\\sqrt{2}", "decimal": "21.21320…", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$30\\sin\\left(45^{\\circ\\:}\\right)=15\\sqrt{2}$$", "input": "30\\sin\\left(45^{\\circ\\:}\\right)", "steps": [ { "type": "interim", "title": "Use the following trivial identity:$${\\quad}\\sin\\left(45^{\\circ\\:}\\right)=\\frac{\\sqrt{2}}{2}$$", "input": "\\sin\\left(45^{\\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{\\sqrt{2}}{2}" } ], "meta": { "interimType": "Trig Trivial Angle Value Title 0Eq" } }, { "type": "step", "result": "=30\\cdot\\:\\frac{\\sqrt{2}}{2}" }, { "type": "interim", "title": "Simplify $$30\\cdot\\:\\frac{\\sqrt{2}}{2}:{\\quad}15\\sqrt{2}$$", "input": "30\\cdot\\:\\frac{\\sqrt{2}}{2}", "result": "=15\\sqrt{2}", "steps": [ { "type": "step", "primary": "Multiply fractions: $$a\\cdot\\frac{b}{c}=\\frac{a\\:\\cdot\\:b}{c}$$", "result": "=\\frac{\\sqrt{2}\\cdot\\:30}{2}" }, { "type": "step", "primary": "Divide the numbers: $$\\frac{30}{2}=15$$", "result": "=15\\sqrt{2}" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7SWcRpVmQKefhpjnTjmawr1P2FVutOfIuyxdOGlLsYk8tOtZYwUjyXhDTsNnn6Elr/Kj+Q69gnzVE9VBbVyDS8H70HMrwpajnQAPgMdJ27vpN5Aod6Hr1Lp2e/29KhSgUp+grc5tSnXM3hsN6n7DW79soC7AehXd6wZc5g4AHhVnURff1gC8ZCE/0cK/WvHpf" } } ], "meta": { "solvingClass": "Trig Evaluate", "practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Evaluate%20Functions", "practiceTopic": "Evaluate Functions" } }, "meta": { "showVerify": true } }