periodicity of f(x)=cos(1/5 x)

{ "query": { "display": "periodicity $$f\\left(x\\right)=\\cos\\left(\\frac{1}{5}x\\right)$$", "symbolab_question": "FUNCTION#periodicity f(x)=\\cos(\\frac{1}{5}x)" }, "solution": { "level": "PERFORMED", "subject": "Functions & Graphing", "topic": "Functions", "subTopic": "periodicity", "default": "10π", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "Periodicity of $$\\cos\\left(\\frac{1}{5}x\\right):{\\quad}10π$$", "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|\\frac{1}{5}\\right|}" }, { "type": "step", "primary": "Simplify", "result": "=10π" } ], "meta": { "solvingClass": "Function Periodicity" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "\\cos(\\frac{1}{5}x)" }, "showViewLarger": true } }, "meta": { "showVerify": true } }