The basic strategy is to iterate over a 80x12 table of data, and for each item determine whether it appears on the sine wave, plotting the next letter in the repeating 'japh' sequence if so.

The column index is treated as degree / 4.5, which yields 360 degrees for 80 columns.
Radian = Column * 4.5 * pi / 180. The coordinate system is very coarse, so not much precision is needed. Reduced as follows:

radian = column * 4.5 * 3.14 / 180
radian = column * 0.0785
radian = column * 0.1

To golf a bit I keep track of the current column by pushing another value onto @$a in each column, and using $#$a for the current column index. Easier and more efficient to just use the value of $_... but it amused me.

Using the sin * 6, and subtracting 6 from the current row ($b) is done to provide a +-6 vertical range for the sin wave.