Intersection of sine and cosine

Find where $y = \sin x$ and $y = \cos x$ meet. Dividing $\sin x = \cos x$ by $\cos x$ gives $\tan x = 1$, which holds when $x = \dfrac{\pi}{4} + n\pi$ for an integer $n$.

For example, at $x = \dfrac{\pi}{4}$ both equal $\dfrac{\sqrt{2}}{2}$, and at $x = \dfrac{5\pi}{4}$ both equal $-\dfrac{\sqrt{2}}{2}$. The large dots mark these two crossings; the curves keep meeting every $\pi$ thereafter.