Question

f(x,y)=sinx+siny
Plot the gradient vector field of "f" together with a contour map of "f". Explain how they are related
to each other.

Here is my gradient vector field:
\[\nabla f(x,y)=\frac{\partial f}{\partial x}\hat i +\frac{\partial f}{\partial y}\hat j\]
\[=cosx \hat i+cosy \hat j\]

Answer 1

gradient vectors are perpendicular to the level curves

Answer 2

Is that image specific to cosx i+cosy j?

Answer 3

so the relationship is that gradient vectors are perpendicular to the level curves on the contour map