Question

3 \sin(x) + 3 \cos(y) - 3 \sin(x) \cos(y) + x = {6 \pi} at the point ( 6\pi,5\pi/2 ).

Answer 1

\[
3 \sin(x) + 3 \cos(y) - 3 \sin(x) \cos(y) + x \\
x = 6\pi, ~~ y =5\pi/2 \\
3 \sin(6\pi) + 3 \cos(5\pi/2 ) - 3 \sin(6\pi) \cos(5\pi/2 ) + 6\pi = \\
0 + 3 \cos(\pi/2 ) - 0 + 6\pi = 6\pi
\]

Answer 2

\[
6\pi = 3 * 2\pi = 3*2\pi + 0 ~~~~ \text{(Three full rotations and so it back to 0 degrees.)} \\
5\pi/2 = (4\pi+\pi)/2 = 2\pi + \pi/2
~~~~ \text{(One full rotation plus pi/2. It is 90 degrees.)} \\
\]