Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 131

\[1)\ y = 12\sin x - 5\cos x\]

\[c = \sqrt{12^{2} + 5^{2}} = \sqrt{169} = 13;\]

\[y = 13\left( \frac{12}{13}\sin x - \frac{5}{13}\cos x \right) =\]

\[= 13\sin\left( x - \arccos\frac{12}{13} \right).\]

\[E(y) = \lbrack - 13;\ 13\rbrack.\]

\[2)\ y = \cos^{2}x - \sin x\]

\[y = 1 - \sin^{2}x - \sin x\]

\[y = - \left( \sin^{2}x + \sin x + \frac{1}{4} \right) + \frac{5}{4}\]

\[y = - \left( \sin x + \frac{1}{2} \right)^{2} + \frac{5}{4}.\]

\[- 1 \leq \sin x \leq 1\]

\[- \frac{1}{2} \leq \sin x + \frac{1}{2} \leq \frac{3}{2}\]

\[- \frac{9}{4} \leq - \left( \sin x + \frac{1}{2} \right)^{2} \leq 0\]

\[- 1 \leq \frac{5}{4} - \left( \sin x + \frac{1}{2} \right)^{2} \leq \frac{5}{4}.\]

\[E(y) = \left\lbrack - 1;\ \frac{5}{4} \right\rbrack.\]