For the potential function $(x,y)=-y+sinx$ and points $A=(\frac{}{2},1),B=(,0),C=$

$(3\frac{}{2},-1)$ and $D=(2,0)on$ the level curve $(x,y)=0,$ complete the following steps.

$(a)$ Find the gradient field $F=$grad$.$

$(b)$ Evaluate $Fat$ the points $A,B,C,$ and $D.$

$(c)$ Plot the level curve $(x,y)=0$ and the vectors $Fat$ the points $A,B,C,$ and $D.$