{ "query": { "display": "$$0+\\cos\\left(2\\right)\\left(0\\right)+e^{-4}$$", "symbolab_question": "TRIG_EVALUATE#0+\\cos(2)(0)+e^{-4}" }, "solution": { "level": "PERFORMED", "subject": "Trigonometry", "topic": "Evaluate Functions", "subTopic": "Simplified", "default": "\\frac{1}{e^{4}}", "decimal": "0.01831…", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$0+\\cos\\left(2\\right)\\left(0\\right)+e^{-4}=\\frac{1}{e^{4}}$$", "input": "0+\\cos\\left(2\\right)\\left(0\\right)+e^{-4}", "steps": [ { "type": "step", "result": "=0+\\cos\\left(2\\right)\\cdot\\:0+e^{-4}" }, { "type": "interim", "title": "$$0+\\cos\\left(2\\right)\\cdot\\:0+e^{-4}=\\frac{1}{e^{4}}$$", "input": "0+\\cos\\left(2\\right)\\cdot\\:0+e^{-4}", "steps": [ { "type": "step", "primary": "Apply rule $$0\\cdot\\:a=0$$", "result": "=0+0+e^{-4}" }, { "type": "interim", "title": "Simplify", "input": "0+0+e^{-4}", "steps": [ { "type": "step", "primary": "Apply exponent rule: $$a^{-b}=\\frac{1}{a^b}$$", "secondary": [ "$$e^{-4}=\\frac{1}{e^{4}}$$" ], "result": "=0+0+\\frac{1}{e^{4}}", "meta": { "practiceLink": "/practice/exponent-practice", "practiceTopic": "Expand FOIL" } }, { "type": "step", "primary": "$$0+0=0$$", "result": "=\\frac{1}{e^{4}}" } ], "meta": { "interimType": "Generic Simplify 0Eq" } }, { "type": "step", "result": "=\\frac{1}{e^{4}}" } ], "meta": { "solvingClass": "Solver", "interimType": "Solver" } }, { "type": "step", "result": "=\\frac{1}{e^{4}}" } ], "meta": { "solvingClass": "Trig Evaluate", "practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Evaluate%20Functions", "practiceTopic": "Evaluate Functions" } }, "meta": { "showVerify": true } }