Phase and Time shifting a Cosine and a Sine.

Cuthbert Nyack
A sine has a phase of 0 at t = 0 and a cosine has a phase of p/2 at t = 0.
The applet below shows how a cosine (green) and a sine (red) are affected as their phases are changed.
When their phases are advanced by 90°, the sine becomes a cosine and the cosine becomes a negative sine. Equivalent to differentiating.
When their phases are delayed by 90°, the sine becomes a negative cosine and the cosine becomes a sine. Equivalent to integrating.




The applet below shows how a cosine (green) and a sine (red) are affected as they are time shifted.
When they are advanced by 0.25T, the sine becomes a cosine and the cosine becomes a negative sine. Equivalent to differentiating.
When they are delayed by 0.25T, the sine becomes a negative cosine and the cosine becomes a sine. Equivalent to integrating.




When activated the following gif image show how the applet should appear.

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COPYRIGHT 2007 Cuthbert Nyack.