Properties of y = cos x and its graph

$y=\cos x$ and the phase shift of sine

$\cos x=\sin\left(x+\dfrac{\pi}{2}\right)$ for all $x\in\mathbb{R}$ . Hence the graph of $y=\cos x$ comes from $y=\sin x$ by a parallel shift along $Ox$ by $-\dfrac{\pi}{2}$ (equivalently, shift sine by $+\dfrac{\pi}{2}$ in the argument). $D(\cos)=\mathbb{R}$ , $E(\cos)=[-1;1]$ . Zeros: $\cos x=0 \Leftrightarrow x=\dfrac{\pi}{2}+\pi k,\ k\in\mathbb{Z}$ .

$\cos$ is even: $\cos(-x)=\cos x$ ⇒ symmetry of the graph about the $Oy$ axis

Content is available with subscription.

Get full access to all courses on the platform for one year with a single payment.

Unlike other platforms that charge per course, here you get everything for one price, and after one year of use there will be no automatic charge for the following year.