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Anti-trigonometry Function

Source: 1997 National High School Mathematics League, Exam One, Problem 5

March 4, 2020
functiontrigonometry

Problem Statement

Let f(x)=x2−πxf(x)=x^2-\pi x, α=arcsin⁡13,β=arctan⁡54,γ=arccos⁡(−13),δ=arccot(−54)\alpha=\arcsin\frac{1}{3},\beta=\arctan\frac{5}{4},\gamma=\arccos\left(-\frac{1}{3}\right),\delta=\text{arccot}\left(-\frac{5}{4}\right) (A)f(α)>f(β)>f(δ)>f(γ)\text{(A)}f(\alpha)>f(\beta)>f(\delta)>f(\gamma) (B)f(α)>f(δ)>f(β)>f(γ)\text{(B)}f(\alpha)>f(\delta)>f(\beta)>f(\gamma) (C)f(δ)>f(α)>f(β)>f(γ)\text{(C)}f(\delta)>f(\alpha)>f(\beta)>f(\gamma) (D)f(δ)>f(α)>f(γ)>f(β)\text{(D)}f(\delta)>f(\alpha)>f(\gamma)>f(\beta)
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