From the graph below we see that the tangent to the curve y = cos x at the point (0, 1) is horizontal and, thus, its slope is 0.

This is not 100% sure. Because cos x <= 1 and cos 0 = 1 we know that if the curve y = cos x does have a propoer tangent at the point (0, 1) then the tangent would have to be horizontal as it appears in the picture. But there are curves that do not have proper tangents. For example, the curve y = |x| does not have a proper tangent at the point (0, 0) because at that point there is a sharp point or corner on the curve.