Answer
avg value $ = 2.5$
rms $ = 2.872$
Work Step by Step
Start by writing down $T = 2* \pi /w$
Next use the integral formula for average value on the signal
$avg = \frac{w}{2* \pi} * \int ^{(2* \pi/w}_{0} {2*cos(w*t)+2.5)dt}$
Evaluate the integral and see that the values of w cancel out and all that is left is 2.5
$avg = 2.5$
Calculate rms by using the square root of the integral of the signal squared times frequency
$rms = \sqrt{ w/(2* \pi) \int ^{\frac{2 \pi}{w}}_0 {(4*cos^2 (wt) + 10*cos(wt) +6.25)dt}}$
Evaluate the integral
$rms = \sqrt{33/4}$
rms = 2.872
