How do i distinguish cosine and sine functions

[supernova1203]

How do i distinguish between a cosine and sine function simply by looking at the graph? Usually its easy because the graph for the base sine and cosine functions have certain distinctive features(like cosine function intercepts the y-axis at 1 usually) and the sine function hits the origin(0,0)

but once they start transforming these functions, stretching/shifting, i can sometimes not tell the difference sin functions usually look smooth like hills and cosine functions look like the udders of a cow @_@

 

[eumyang]

There really isn't a difference in terms of the basic shape of the graph. The graph of the cosine function is itself a transformation of the graph of the sine function.
$$\cos x = \sin \left(x + \frac{\pi}{2} \right)$$

Any cosine function can be rewritten as a sine function with a horizontal translation. In my pre-calculus class we label all of these graphs as sinusoids, based on the sine function only, in the form
$$f(x) = a \sin (b(x - h)) + k$$

 

[QuarkCharmer]

They are exactly the same thing. Ordinarily, you would use the simplest form, the one closest to 0 radians. Sometimes questions like to specify a range, asking you to give the equation where -C/B is between M and N radians.

-C/B from the form asin(bx+c) + k