Progmem store a data (sin table) to code memory space (flash), 32k

LUT is very convenient way to improve math performance on 8-bit controllers, I used progmem also for Hamming and Bit-Reverse tables in other my projects ( N=512 FFT ).

For OP, actually, he doesn't need high speed math, for 1 sec using regular sin function code is just fine:

` `

int sin_value = 16383 *sin(( angle * frequecy * 2 * 3.1415926535 / FFT_SIZE)

int cos_value = 16383 *cos(( angle * frequecy * 2 * 3.1415926535 / FFT_SIZE)