Which of the following functions has a period | vedclass

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(D) The period of the function $\cos (kx)$ is given by $T = \frac{2 \pi}{|k|}$.We check each option:$A) \cos \left( \frac{\pi}{3} x \right) \implies T

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$\cos (\pi x)$

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(D) The period of the function $\cos (kx)$ is given by $T = \frac{2 \pi}{|k|}$.We check each option:$A) \cos \left( \frac{\pi}{3} x \right) \implies T = \frac{2 \pi}{\pi/3} = 6$.$B) \cos \left( \frac{\pi}{2} x \right) \implies T = \frac{2 \pi}{\pi/2} = 4$.$C) \cos (2 \pi x) \implies T = \frac{2 \pi}{2 \pi} = 1$.$D) \cos (\pi x) \implies T = \frac{2 \pi}{\pi} = 2$.Therefore,the function with period $2$ is $\cos (\pi x)$.

Which of the following functions has a period of $2$?

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