Why do we get cos(x) when we differentiate sin(x)?

If we have an equation for a line, it follows a certain shape when put it on Cartesian axes. If we wish to find the value of the gradient of the graph at a certain coordinate, we can use differentiation to give us a numerical value. The easiest visualisation of differentiation is to look at the graphs y=sin(x) and y=cos(x). When we differentate sin, we get cos; as each cos point corresponds to the value of the gradient at each sin point. Where the gradient of sin is 0 (where the tangent to the curve is a horizontal line), for the same x value, the y value of a cos curve is also 0.