Final answer:
To find the periods of the signals x(t) = -2 + (1/2) * cos((5/6)t + 20°) + cos((7/3)t), we use the formula T = 2π/ω. The resulting periods are 12π/5 for the first term and 6π/7 for the second term, respectively.
Step-by-step explanation:
The period of a signal is the duration of one full cycle of the wave. To find the period of the given signals, we look at the angular frequency component of each cosine term. The general form for a cosine function is cos(ωt + φ), where ω is the angular frequency. The period (T) of the wave is given by 2π/ω. For the first term cos((5/6)t + 20°), the angular frequency is (5/6) and for the second term cos((7/3)t), it is (7/3).
To find the periods of these functions, we calculate:
- For cos((5/6)t + 20°), the period T is 2π/(5/6) which simplifies to 12π/5.
- For cos((7/3)t), the period T is 2π/(7/3) which simplifies to 6π/7.
Therefore, the periods of the signals are 12π/5 and 6π/7 respectively.