Question

How to convert sine to cosine.? if i have the following equation: y = sin (300t and i want to represent this as a cos?

Answer 1

If you were to graph the sine and cosine functions on the same set of axes, you'd see that they are 90 degrees, or pi/2 radians, out of sync with one another.  cos 0 is 1, whereas sin 0 is 0; sin x does not reach the value 1 until your angle reaches 90 degrees, or pi/2 radians.

Please do some experimentation here.  You want to express sin (300t) as a cosine, that is, as cos (300t + [some angle]), where [some angle] is called a "phase shift."

Start with the basic y=sin x.  Its graph is usually begun at (0,0).  Try simplifying and graphing cos (x-pi/2).  Does this produce the same y=sin x, with the same graph?  Do you remember that 
  cos (x-pi/2) = cos x cos pi/2 + sin x sin pi/2?
It happens that cos pi/2 = 0 and that sin pi/2 = 1.  Thus,
  cos (x-pi/2) = sin x (1) = sin x.  So, we have succeeded in obtaining sin x from cos (x-pi/2).

Now, what about obtaining sin 300t from the cosine function?

First:  recognize that the standard form of the cosine function with a phase shift is     y = a cos (bx + c).  What is the period?

Answer:  The period is always 2pi/b.  So, in the case, the period is 2pi/300, or pi/150.

What is the phase shift?
Answer:  the period is always -c/b.  So, in this case, the period is -c/b, or 
-pi/2 over 300.  This simplifies to -pi/150.

Try this:  Simplify cos (300t -pi/150)  If the end result is sin 300t, you'll know you have this right.  If the end result is not sin 300t, experiment with that phase shift.