Wave cancellation and reinforcement for tangential forces?

Question

Wave propagation theory shows that positive forces are additive to negative forces effectively canceling them or reinforcing them dependant upon phase.
For example: sin(x) - sin(x) = 0 (on same domain).

The theory also shows that an electrical (E) and magnetic (H) component are present at right angles to one another when inducing current through wire (right-hand rule). Say an apparatus were designed to generate the E and H components separately then feed them to the same line 90 degrees out of phase, would this induce a tangent waveform perpendicular to the line because every 180 degrees the fields would collapse if one were to use the definition sin(x)/cos(x) = tan(x)?

Now if that premise were correct, cut the line to introduce a standing wave that would cancel the E and H fields to produce a null field. Is this an example of tan(x) - tan(x) = 0? If so, then this would produce the case of tan(pi/2) - tan(pi/2) = 0.

Answer 1

No, this procedure does not produce a waveform that is proportional to tan(x).

You made an error when you decided to divide the electric field by the magnetic field, and wrote sin(x)/cos(x). There is no reason to do a division here.

I can't even think of a situation where it would make sense to divide by a magnetic field. H is a vector quantity, and vectors are not something that we divide by.

Answer 2

wow,nice math doing,i proofed it and got all the same answers,but um hows this a question?