Calculating the Average Power of a Signal

[jegues]

Homework Statement

Find the average power of the signal,

$$x_{1}(t) = 5cos(2\pi t + \frac{\pi}{10}) - 6sin(10t + \frac{\pi}{8})$$

Homework Equations

The Attempt at a Solution

$$P_{avg} = \frac{1}{T_{1}} \int_{0}^{T_{1}} 25dt + \frac{1}{T_{2}}\int_{0}^{T_{2}}36dt$$

$$P_{avg} = 61$$

The answer they list is,

$$P_{avg} = \frac{61}{2}$$

Why are they using the RMS value of the signal as the magnitude?

 

[tiny-tim]

hi jegues!

eg 25*cos*sin = (25/2)*sin2, so its average is 25/2