Energy
Energy of cos(2t) from t= 0 to $ 2\pi $
$ E = \int_{t1}^{t2}{|(f(t)|^2}dt $
$ E = \int_{0}^{2\pi}{|cost(2t)|^2}dt $
$ E = \frac{1}{2} \int_{0}^{2\pi}{|cost(4t)|^2}dt $
$ E = \frac{1}{2} (t + \frac{1}{4}(sin(4t))| t= 0 to 2\pi $
$ E = \frac{1}{2} (2\pi + 0) $
$ E = \pi $
Power
Power of cos(2t)
$ P = \frac{1}{t2-t1}\int_{t1}^{t2}{|f(t)|^2}dt $
$ P = \frac{1}{2\pi-0}\int_{0}{2\pi}{|cos(2t)|^2}dt $
$ P = \frac{1}{2\pi} * E $
$ P = \frac{1}{2\pi} * \pi $
$ P = \frac{1}{2} $
