{ "query": { "display": "periodicity $$f\\left(x\\right)=2\\cos\\left(πx\\right)$$", "symbolab_question": "FUNCTION#periodicity f(x)=2\\cos(πx)" }, "solution": { "level": "PERFORMED", "subject": "Functions & Graphing", "topic": "Functions", "subTopic": "periodicity", "default": "2", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "Periodicity of $$2\\cos\\left(πx\\right):{\\quad}2$$", "steps": [ { "type": "step", "primary": "Periodicity of $$a\\cdot\\cos\\left(bx\\:+\\:c\\right)\\:+\\:d=\\frac{\\mathrm{periodicity\\:of}\\:\\cos\\left(x\\right)}{|b|}$$", "secondary": [ "Periodicity of $$\\cos\\left(x\\right)\\:$$is $$2π$$" ], "result": "=\\frac{2π}{\\left|π\\right|}" }, { "type": "step", "primary": "Simplify", "result": "=2" } ], "meta": { "solvingClass": "Function Periodicity" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "2\\cos(πx)" }, "showViewLarger": true } }, "meta": { "showVerify": true } }