A Bounded Trig Image

★ 8/10trigonometry Extrema Substitution Absolute Value inequality

Problem

Let $a, b, c \in \mathbb{R}$ , and suppose

\left|a\cos^2 x + b\sin x + c\right| \leqslant 1 \qquad \text{for all } x \in \mathbb{R}.

Find the maximum possible value of $|a\sin x + b|$ over all $x$ and all such $a, b, c$ .

Answer

Solution

Difficulty	8/10
Topics	trigonometry, Extrema, Substitution, Absolute Value, inequality

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