Ageneral expression for an electromagnetic plane wave can be written as e asin( k-r-cot) + b cos( k . r-ot) or e dsin( k . r-dot + α). find d and α in terms of a and b.

and

Explanation:

Hi! Since the notation is a little bit messed up, I am going to suppose that

  --- (1)

and :

 --- (2)

Here we are going to use a trigonometric identity of the sine of the sum of two angles, namely:

--- (3)

Lets set:

So now (2) becomes:

 --- (4)

Now (1) and (4) must be equal, and in particular we must have the following identities:

  --- (5)

If we square these two identities and sum them we got:

And since:

We got the first solution:

For the second part we must divide the identies (5)

We got:

And since:

We use the inverse of the tan function:

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