Respuesta :

calculista

using a graph tool

I proceed to graph each case


case a)

[tex] y=cos (\frac{1}{2} x) [/tex]

see the attached figure N 1


case b)

[tex] y=cos (\frac{1}{4} x) [/tex]

see the attached figure N 2


case c)

[tex] y=cos (4x) [/tex]

see the attached figure N 3


case d)

[tex] y=cos (2x) [/tex]

see the attached figure N 4


therefore


the answer is the option A

[tex] y=cos (\frac{1}{2} x) [/tex]

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frika

The period of the function [tex] y=\cos (kx) [/tex] is [tex] T=\dfrac{2\pi }{k} [/tex]. From the graph you can see that period of given function is [tex] 4\pi [/tex] (you can see that at x=0, y=1 and next time y=1 when x=4π ).


Then 

[tex] 4\pi =\dfrac{2\pi}{k} ,\\ 4\pi k=2\pi,\\ k=\dfrac{2\pi }{4\pi } =\dfrac{1}{2} [/tex].


For [tex] k=\dfrac{1}{2} [/tex] the function [tex] y=\cos (kx) [/tex] becomes [tex] y=\cos (\dfrac{1}{2} x) [/tex].


Answer: correct choice is A.

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