Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I am trying to figure out what the result is when adding two sinusoids of the same frequency but with different phase and amplitudes. Specifically I want to know if the result is always another sinusoid of the same frequency. For the case of the the same amplitude I have:

cos(wt) + cos(wt+phi) = 2.cos(wt+phi/2).cos(phi/2) ... this follows from the trig. identity:

cos(A)+cos(B) = 2.cos[(A+B)/2].cos[(A-B)/2]

So the addition of two sinusoids of the same frequency and amplitude will always give a sinusoid of the same frequency. What about the more general case:

cos(wt) + k.cos(wt+phi) where k is a constant. Will the result here also always be a sinusoid of frequency w ? Intuitively I think so, but I havn't been able to derive an expression for the phase and amplitude.

Does anyone know ?

Thanks.

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Is there a trigonometric identity for this ?

Loading...

Similar Threads - trigonometric identity | Date |
---|---|

B Trigonometric identities | Oct 10, 2017 |

I Infinite series of trigonometric terms | Sep 30, 2017 |

I Question ,trigonometric identities equation and functions ? | Jul 12, 2016 |

I Is this a Trigonometric Identity? | Jul 7, 2016 |

What are trigonometric identities | Jul 23, 2014 |

**Physics Forums - The Fusion of Science and Community**