Geometry
# Graphs of Trigonometric Functions

Consider two functions $f(x)=25-\sin 6x, g(x)=\left\lfloor \frac{x}{2} \right\rfloor.$ Find the sum of all the elements in the range of $g(f(x))$.

**Details and assumptions**

The function $\lfloor x \rfloor: \mathbb{R} \rightarrow \mathbb{Z}$ refers to the greatest integer smaller than or equal to $x$. For example, $\lfloor 2.3 \rfloor = 2$ and $\lfloor -5 \rfloor = -5$.

The graph of $y=7 \tan (2\pi x-\pi)+18$ has period $\frac{1}{a}$. What is the value of $a$?

What is the sum of the maximum and minimum values of the function $y=|\sin x-7|+20?$