7cos(90)+4sin(180+pi/3)

{ "query": { "display": "$$7\\cos\\left(90^{\\circ\\:}\\right)+4\\sin\\left(180^{\\circ\\:}+\\frac{π}{3}\\right)$$", "symbolab_question": "TRIG_EVALUATE#7\\cos(90^{\\circ })+4\\sin(180^{\\circ }+\\frac{π}{3})" }, "solution": { "level": "PERFORMED", "subject": "Trigonometry", "topic": "Evaluate Functions", "subTopic": "Simplified", "default": "7\\cos(\\frac{π}{2})+4\\sin(\\frac{4π}{3})", "decimal": "-3.46410…", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$7\\cos\\left(90^{\\circ\\:}\\right)+4\\sin\\left(180^{\\circ\\:}+60^{\\circ\\:}\\right)=7\\cos\\left(90^{\\circ\\:}\\right)+4\\sin\\left(240^{\\circ\\:}\\right)$$", "input": "7\\cos\\left(90^{\\circ\\:}\\right)+4\\sin\\left(180^{\\circ\\:}+60^{\\circ\\:}\\right)", "steps": [ { "type": "step", "primary": "Rewrite as", "result": "=\\sin\\left(2\\cdot\\:120^{\\circ\\:}\\right)" }, { "type": "interim", "title": "Rewrite using trig identities:$${\\quad}\\sin\\left(2\\cdot\\:120^{\\circ\\:}\\right)=2\\sin\\left(120^{\\circ\\:}\\right)\\cos\\left(120^{\\circ\\:}\\right)$$", "input": "\\sin\\left(2\\cdot\\:120^{\\circ\\:}\\right)", "result": "=7\\cos\\left(90^{\\circ\\:}\\right)+4\\sin\\left(180^{\\circ\\:}+60^{\\circ\\:}\\right)", "steps": [ { "type": "step", "primary": "Use the Double Angle identity: $$\\sin\\left(2x\\right)=2\\sin\\left(x\\right)\\cos\\left(x\\right)$$", "result": "=2\\sin\\left(120^{\\circ\\:}\\right)\\cos\\left(120^{\\circ\\:}\\right)" } ], "meta": { "interimType": "Trig Rewrite Using Trig identities Title 0Eq" } }, { "type": "step", "primary": "Simplify", "result": "=7\\cos\\left(90^{\\circ\\:}\\right)+4\\sin\\left(240^{\\circ\\:}\\right)" } ], "meta": { "solvingClass": "Trig Evaluate", "practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Evaluate%20Functions", "practiceTopic": "Evaluate Functions" } }, "meta": { "showVerify": true } }