Find-the-period-of-f-x-where-f-x-cos-2x-pi-3-sin-3x-2-pi-4-How-may-one-find-the-period-of-the-following-functions-if-x-has-period-m-and-x-has-period-n-1-f-1-x-x-x-2-f-2-x

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Question Number 1812 by 112358 last updated on 04/Oct/15

$$Findtheperiodoff\left(x\right)where$$$$f\left(x\right)=cos(2x+\frac{\pi }{3})+sin(\frac{3x}{2}-\frac{\pi }{4}).$$$$Howmayonefindtheperiod$$$$ofthefollowingfunctions$$$$if\psi \left(x\right)hasperiodmand\gamma \left(x\right)$$$$hasperiodn?$$$$\left(1\right)f_1\left(x\right)=\psi \left(x\right)\gamma \left(x\right)$$$$\left(2\right)f_2\left(x\right)=\frac{\psi \left(x\right)}{\gamma \left(x\right)}\{\gamma \left(x\right)\ne 0\}$$$$\left(3\right)f_3\left(x\right)={\left\{\psi \left(x\right)\right\}}^{\gamma \left(x\right)}$$$$\left(4\right)f_4\left(x\right)={log}_{\psi \left(x\right)}\gamma \left(x\right)$$$$\left(5\right)f_5\left(x\right)=\psi \left(x\right)\pm \gamma \left(x\right)$$$$\left(6\right)f_6\left(x\right)=cos\left(\psi \left(x\right)\gamma \left(x\right)\right)$$$$$$

Answered by 123456 last updated on 06/Oct/15

$$\mathrm{\exists }(s,t)\in {\mathbb{Z}}^2,sm=tn$$$$\left(1\right),\left(2\right)and\left(5\right)wouldhaveperiodlcm(m,n)$$$$$$

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