Question

we know that derivative of sin(x) is cos(x) and also that derivative represents slope to the curve at particular point.
i am not able to connect both of the above statements together ?????

Answer 1

Perhaps it will help to look at a graph showing both functions. In the attached image, when the sine (red curve) crosses the y-axis, it slopes upward at about a 45 degree angle. If the scale of the x-axis matched the scale of the y-axis this would be exactly 45 degrees, which means the curve has a slope of 1 at that point. In that same place (that is, at the y-axis), the cosine (blue line) has value 1, so the value of the cosine matches the slope of the sine curve.

Move to the right a little and you'll see the red sine curve level off, so its slope at that point has to be zero. At this point the blue cosine curve crosses the x-axis, so the value of the cosine is zero when the slope of the sine is zero. The value of the cosine will always match the slope of the sine curve, and that's what it means to say that the cosine is the derivative of the sine.