The sine function $f(x)=\sin(x)$ is the function that adds the sine of $x$ to each number $x$.

As we have seen in the unit circle, the function repeats every $2 \pi$. We therefore call the sine function a periodic function with $\blue{\text{period}}$ $2 \pi$.

The function also has an $\green{\text{equilibrium}}$. This is the middle of the function, or the $y$-value that lies exactly between the highest and the lowest point. For the sine function, this is $0$.

Finally, the $\purple{\text{amplitude}}$ of the function is equal to $1$. This means that the value between the equilibrium and the highest point (or the lowest point) equals $1$.

The cosine function $f(x)=\cos(x)$ is the function that adds the cosine of $x$ radians to each number $x$.

Like the sine function, the cosine function is a periodic function. This too has $\blue{\text{period}}$ $2\pi$.

The $\green{\text{equilibrium}}$ is equal to $0$.

Additionally, the $\purple{\text{amplitude}}$ of the function is equal to $1$.

When we compare the cosine function with the sine function, we see that the graphs are very similar. When we move the cosine function to the right by $\frac{\pi}{2}$, we have the sine function.

The tangent function $f(x)=\tan(x)$ is the function that adds the tangent of $x$ radians to each number $x$.

Like the sine and cosine functions, the tangent function is a periodic function. The $\blue{\text{period}}$ is equal to $\pi$.

The vertical asymptotes of the tangent function are $x=\frac{\pi}{2}+k \cdot \pi$, in which $k$ is an integer, as for the $x$-values $\frac{\pi}{2}$, $\frac{3 \pi}{2}$ and $\frac{5 \pi}{2}$, but also for $\frac{-3 \pi}{2}$.