The FIND_COSINE subroutine starts by reading the given angle, THETA, from on-chip RAM. This would likely be done using direct addressing, because RAM on most 68HC05 devices is located below $00FF. There is usually no explicit need to denote whether an instruction should use direct or extended addressing - most assemblers will make this determination automatically, based on the value to which the symbol THETA is equated.
THETA is loaded into the index register and shifted right two places (effectively dividing it by four) and used with the offset COSINE_TABLE, to read the cosine of the first known angle less than THETA. The value at COSINE_TABLE + 1 subtracted from the accumulator would be the cosine of the first known angle greater than THETA. The offset COSINE_TABLE can be eight or sixteen bits, and as with THETA, most assemblers will determine which addressing mode should be used.
The difference between the cosines of the first known angles less than and greater than THETA is then divided by four (again, using two right shift instructions). Next, it is transferred to the index register where it will be multiplied by the difference between THETA and the first known angle less than THETA.