Sine, Cosine and Tangent Curves

Sine curve

\[y=\sin x\]

The \(x\)-intercepts occur at \(x=k\pi\), \(k\in\mathbb{Z}\). Turning points occur at \(x=\dfrac{2k+1}{2}\pi\), where \(2k+1\) is odd.

Cosine curve

\[y=\cos x\]

The \(x\)-intercepts occur at \(x=\dfrac{2k+1}{2}\pi\), \(k\in\mathbb{Z}\). Turning points occur at \(x=k\pi\).

Tangent curve

\[y=\tan x\]

The \(x\)-intercepts occur at \(x=k\pi\), \(k\in\mathbb{Z}\). The lines \(x=\dfrac{2k+1}{2}\pi\) are vertical asymptotes, where \(2k+1\) is odd.