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The power of a deterministic signal $s(t)$ is given by $$P_s=\lim_{T\to\infty}\frac{1}{2T}\int_{-T}^Ts^2(t)dt\tag{1}$$ A unit power signal is obtained by normalizing $s(t)$ by the root of its power: $$\hat{s}(t)=\frac{s(t)}{\sqrt{P_s}}\tag{2}$$ In the case of $s(t)=A\cos(2\pi f_0t)$ you obtain from $(1)$ P_s=\lim_{T\to\infty}\frac{1}{2T}\int_{-T}^TA^2\cos^...