The rms(root-mean-square) value of a periodic signal s(t) is defined to be

Question

rms [s]=(1/T Ss^2t dt)^1/2
where T is defined to be the signal's period: the smallest positive number such that s(t)=s(t+T).

What is the rms value of the sinusoid s(t)=Asin(2πf0t)? (Again, write A as A and f0 as f0.)

Answer 1

The rms value of a sine function of amplitude A is A/sqrt2 = 0.70711 A.

That can be derived from the definition you were given.