question_answer

Are the functions \[\text{tan  }\!\!\omega\!\!\text{ t}\] and \[\mathbf{cot \omega t}\] periodic? Are they harmonic?

Answer:

                Both\[\text{tan  }\!\!\omega\!\!\text{ t}\] and \[\cot \omega t\]are periodic functions each with period\[T=\pi /\omega \], because \[\tan \left[ \omega \left( t+\frac{\pi }{\omega } \right) \right]=\tan (\omega t+\pi )=\tan \omega t\] and \[\cot \left[ \omega \left( t+\frac{\pi }{\omega } \right) \right]=\cot (\omega t+\pi )=\cot \omega t\] But these functions are not harmonic because they can take any value between 0 and \[\infty \].