A method for composing a lookup table and searching indexes thereof is provided. The method includes the steps of: a) composing a lookup table using a symmetry of a sine and a cosine function; b) changing and setting a gain of a DCO by reflecting a lookup table size in the DCO; c) transforming an absolute value of a DCO output to an integer value; d) determining a range of the integer value of the DCO output; e) searching indexes of a sine and an cosine function according to the range of the integer value of the DCO output; and f) correcting a sign of a lookup table value corresponding to the searched index of the sine function and a sign of a lookup table value corresponding to the searched index of the cosine function according to the range of integers of the DCO output.