frequency 9cos(1/3 x+3/4)

{ "query": { "display": "frequency $$9\\cos\\left(\\frac{1}{3}x+\\frac{3}{4}\\right)$$", "symbolab_question": "FUNCTION#frequency 9\\cos(\\frac{1}{3}x+\\frac{3}{4})" }, "solution": { "level": "PERFORMED", "subject": "Functions & Graphing", "topic": "Functions", "subTopic": "frequency", "default": "\\frac{1}{6π}", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "Frequency of $$9\\cos\\left(\\frac{1}{3}x+\\frac{3}{4}\\right):{\\quad}\\frac{1}{6π}$$", "steps": [ { "type": "definition", "title": "Frequency definition", "text": "For $$f\\left(x\\right)=A{\\cdot}g\\left(Bx-C\\right)+D$$, where $$g\\left(x\\right)$$ is one of the basic trig functions, <br/>the frequency is $$\\frac{B}{2\\pi}$$" }, { "type": "step", "primary": "$$f\\left(x\\right)=9\\cos\\left(\\frac{1}{3}x+\\frac{3}{4}\\right)$$<br/>$$g\\left(Bx-C\\right)=\\cos\\left(\\frac{1}{3}x+\\frac{3}{4}\\right),\\:B=\\frac{1}{3}$$<br/>$$\\frac{B}{2\\pi}=\\frac{\\frac{1}{3}}{2\\pi}$$", "result": "\\frac{1}{6π}" } ], "meta": { "solvingClass": "Function Frequency" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "9\\cos(\\frac{1}{3}x+\\frac{3}{4})" }, "showViewLarger": true } }, "meta": { "showVerify": true } }