Question

What is the period of the function f(x)=cos2x

1/2

π/2

π

2

Answer 1

`\displaystyle \pi`

Explanation:

`\displaystyle f(x) = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow (C)/(B) \\ Wavelength\:[Period] \hookrightarrow (2)/(B)\pi \\ Amplitude \hookrightarrow |A|`

Accourding to the above information, you will have this result:

`\displaystyle \boxed{\pi} = (2)/(2)\pi`

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Answer 2

π

Explanation:

General form of the cosine function is:

`y(x)=Acos(\omega x +\phi)`

Where:

`A= Amplitude\hspace{3} of \hspace{3} the\hspace{3} function\\\omega=Angular\hspace{3} frequency\\\phi=Phase\hspace{3} shift`

The frequency of the function is given by the following equation:

`f=(\omega)/(2 \pi)`

The period is the reciprocal of the frequency, so:

`T=(1)/(f) =(2 \pi)/(\omega)`

From the equation provided, you can see that the angular frequency is 2. Therefore, the periodof the function is:

`T=(2 \pi)/(\omega) =(2\pi)/(2) =\pi`