Final answer:
The period of the signal 2sin(3.142t)+2sin(1.2566t) is not directly available in the choices, but by inferring from the multiples of π, the closest period provided could be option (a) 2, as it is closest to the period of a full sine wave cycle of 2π. However, without the least common multiple of both wave periods, none of the given options accurately reflect the period of the combined signal.
Step-by-step explanation:
The period of a wave is found by taking the reciprocal of the frequency. For a sine wave described by the function sin(bt), the period is given by 2π/|b|, where b is the coefficient of t. In the case of the signal 2sin(3.142t)+2sin(1.2566t), the periods of the individual sine waves are 2π/3.142 and 2π/1.2566 respectively. To find the period of the combined signal, we would need the least common multiple of these two periods. However, in this context, since we are given multiple-choice options, we can infer that the period closest to 2π or approximately 6.283 is likely the correct answer. Option (d) 0.6283 seems to be an error since it doesn't match the periods of the individual waves nor does it represent the period of the combined signal.