TITLE: Period of Trigonometric Functions
QUESTION [6 upvotes]: I have always been taught that in the scenario of a Sine,Tan,Cos function
of $f(x) = a\sin b(x+c) +d$, the period of the sine and cos functions $= \dfrac{2\pi}{b}$, and the period for the tan function $= \dfrac{\pi}{b}$
I don't see how this would apply to trigonometric functions that have powers or trig functions multiplied within the function
e.g $\sin x\tan x + \cos x$...what would be the period?
$\cos^2x\tan x - \sin x$...what would be the period?
Thanks

REPLY [3 votes]: Any expression comprised of functions that all have the same period $t$ with respect to a certain variable is either constant or has a period which divides $t$.  So for example, $\sin(x)^2$ has period $\pi$ which divides $2 \cdot \pi$, the period of $\sin(x)$.