Example 4. Plot the graph of the function $y=\cos x^{2}$.
Solution. It is sufficient to know the points of intersection of the graph of the function $y=\cos x^{2}$ with the $O x$ axis. We have $\cos x^{2}=0$ at $x \pm \sqrt{\frac{\pi}{2}+k \pi}$, $k=0,1,2, \ldots$. At $x= \pm \sqrt{k \pi}, k=1,2,3, \ldots$ we have $\cos x^{2}=(-1)^{k}$. The graph of this function is shown in Fig. 5.15.

![](https://cdn.mathpix.com/cropped/2024_05_22_8f5be56c3f01f571fd60g-057.jpg?height=346&width=924&top_left_y=1195&top_left_x=178)

Fig. 5.15