For \[g(x)=\frac1{6+3\sin x+4\cos x},
\qquad 0^\circ\le x<360^\circ,\] find its maximum and minimum values and the corresponding values of \(x\). Explain why the denominator cannot be zero.
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Answer:Maximum \(1\) at \(216.9^\circ\); minimum \(1/11\) at \(36.9^\circ\); denominator lies in \([1,11]\).