Period

The period $p$ of a function $f(x)$ is the minimum positive value such that $f(x)=f(x+a)\forall x \in \mathbb R$. A common example of a periodic function is $\sin (x)$, which has period $2 \pi$. Note that $f(x+2\pi)=\sin(x+2\pi)=\sin (x)+\cos (2\pi)+\sin (2\pi) \cos (x) = \sin (x)$, so we know that the function repeats every $2\pi$. A diagram can be found at http://www.montereyinstitute.org/courses/DevelopmentalMath/COURSE_TEXT2_RESOURCE/U19_L2_T3_text_final_3_files/image013.gif

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