For example, on a practice exam my professor posted online, she asks for a vecto
ID: 1299342 • Letter: F
Question
For example, on a practice exam my professor posted online, she asks for a vector equation for the total magnetic field (I'll write all the parts of the problem for general clarity but the third part is where I get confused - skip to that part):
C) [This is where I get confused] Assming electromagnetic wave in point P from each antenna is z-polarized and propagates in the +x-direction, write the vector equation for the total magnetic field.
She writes the answer as :
What I, for the life of me, cannot understand is why these are sine functions and not cosine functions as they are written in the book. Please help.
Explanation / Answer
I may not be exactly right on this, however is the only reason I could think of why sine function is used/preferred :
Though both sine and cosine functions are used while representing waves or any harmonic function, but:
sin(-theta) = -sin(theta) and cos (-theta) = cos(theta)
So, in using a sine function we are keeping the information about the argument of function (or theta) preserved, whereas when we use cosine function we lose that information, specially in cases where initial conditions are not known.
e.g., if you are told that the value of E = say +X , given that you know E_0 etc. let that theta be y
E = E_0 sin(y).
Then when we use sine function we will be able to tell exactly what theta is : = y
But when we use cosine function: E=E_0 cos (theta), Now here theta can be both y or -y since ,
E_0 cos (y) = E_0 cos(-y)
So using cosine function we do not get that information. Whereas using sine function that information is captured.
Maybe that is the reason, at some places or in some specific problems where such information is important, sine function is preferred because of its advantage in preserving the theta sign information.
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