Ordering Four Values

★ 6/10functions trigonometry Monotonicity Symmetry

Problem

Let $f(x) = x^2 - \pi x$ , and let

\alpha = \arcsin\frac{1}{3}, \quad \beta = \arctan\frac{5}{4}, \quad \gamma = \arccos\left(-\frac{1}{3}\right), \quad \delta = \operatorname{arccot}\left(-\frac{5}{4}\right).

Arrange $f(\alpha), f(\beta), f(\gamma), f(\delta)$ in decreasing order, with proof.

Answer

Solution

Difficulty	6/10
Topics	functions, trigonometry, Monotonicity, Symmetry

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