Find min $f$ and max $f$ where $x$ and $y$ are real numbers and $f(x,y)=2 \sin x \cos y +3 \sin x \sin y +6 \cos x $ using vectors\matrices? 
Find min $f$ and max $f$ where $x$ and $y$ are real numbers and
  $$f(x,y)=2 \sin x \cos y +3 \sin x \sin y +6 \cos x $$

This question comes from the chapter of my book about vectors and matrices,but frankly I don't see how they come into play.
Can you guys give me some hint ?

Using the Cauchy-Schwarz inequality twice:  $A = 3\sin y + 2\cos y$, then $f(x,y)^2 = (A\sin x+ 6\cos x)^2\leq A^2+6^2 = A^2+36\leq 3^2+2^2+36 = 49 \Rightarrow |f(x,y)| \leq 7$. From this the max is $7$ and the min is $-7$
