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Prove that period of function `f(x)=sinx, x in R " is " 2pi.` |
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Answer» Let period of `f(x)=sin x " be " T` ` :. F(x+T)=f(x)` for all real x. or ` sin(x+T)=sin x` for all real x. ` :. Sin(0+T)=sin 0 " " ("putting" x=0)` ` :. T=n pi, n in Z.` The least value of T is `pi`. But for `T=pi, sin(x+pi)= -sinx ne f(x)` So, let `T=2pi` for which `sin(x+2pi)=sinx.` Thus, period of `sinx` is `2pi`. |
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