C. Consider the nonlinear system x' = sin(x) cos(y) y = – cos(x) sin(y) () T/2 i) Verify that and are equilibrium solutions. T/2 ii) Linearize the system at the equilibrium points in part (i)....

Extracted text: C. Consider the nonlinear system x' = sin(x) cos(y) y = – cos(x) sin(y) () T/2 i) Verify that and are equilibrium solutions. T/2 ii) Linearize the system at the equilibrium points in part (i). Determine whether the equilibrium point is hyperbolic or not. If it is hyperbolic, deter- mine the whether the equilibrium is a source, sink or saddle. iii) Plot the vector field using a vector field plotter.