1. The problem is to find the solutions for the equation $\sin x = \cos x$. 2. We know from trigonometry that $\sin x = \cos x$ means the sine and cosine values of the same angle are equal. 3. Divide both sides by $\cos x$ (assuming $\cos x \neq 0$), we get $\frac{\sin x}{\cos x} = 1$. 4. Using the identity $\tan x = \frac{\sin x}{\cos x}$, we have $\tan x = 1$. 5. The tangent function equals 1 at angles $x = \frac{\pi}{4} + n\pi$ where $n$ is any integer. This is because tangent has period $\pi$. 6. Therefore, the solutions to $\sin x = \cos x$ are $x = \frac{\pi}{4} + n\pi$, for all integers $n$. 7. To plot the graph, plot $y = \sin x$ and $y = \cos x$ on the same axes over an interval (like $[-2\pi, 2\pi]$) and observe where they intersect. Those intersection points correspond to $x = \frac{\pi}{4} + n\pi$. Final answer: The solutions to $\sin x = \cos x$ are all $x$ such that $$x = \frac{\pi}{4} + n\pi, \text{ where } n \in \mathbb{Z}.$$