13) $y = \sin^2x + 2\cos x$
$\to y = 1 - \cos^2x + 2\cos x$
$\to y = - (\cos x - 1)^2 + 2$
Ta có:
$-1\leq \cos x \leq 1$
$\to - 2 \leq \cos x -1\leq 0$
$\to 0 \leq (\cos x -1)^2 \leq 4$
$\to -4 \leq -(\cos x -1)^2 \leq 0$
$\to -2 \leq -(\cos x -1)^2 +2 \leq 2$
Hay $-2 \leq y \leq 2$
Vậy $\min y = -2 \Leftrightarrow \cos x = -1\Leftrightarrow x = \pi + k2\pi$
$\max y = 2 \Leftrightarrow \cos x = 1 \Leftrightarrow x = k2\pi\quad (k\in\Bbb Z)$
14) $y = 3\sin x + 4\cos x - 1$
$\to y +1 = 3\sin x + 4\cos x$
Phương trình có nghiệm
$\Leftrightarrow (y+1)^2 \leq 3^2 + 4^2$
$\Leftrightarrow (y+1)^2 \leq 25$
$\Leftrightarrow - 5 \leq y +1 \leq 5$
$\Leftrightarrow - 6 \leq y \leq 4$
Vậy $\min y = -6;\, \max y = 4$
