MathDB
Anti-trigonometric Function Problem

Source: 1986 National High School Mathematics League, Exam One, Problem 1

February 24, 2020
functioninequalities

Problem Statement

Let −1<a<0-1<a<0, θ=arcsin⁡a\theta=\arcsin a. Then the solution set to the inequality sin⁡x<a\sin x<a is (A){x∣2nπ+θ<x<(2n+1)π−θ,n∈Z}\text{(A)}\{x|2n\pi+\theta<x<(2n+1)\pi-\theta,n\in\mathbb{Z}\} (B){x∣2nπ−θ<x<(2n+1)π+θ,n∈Z}\text{(B)}\{x|2n\pi-\theta<x<(2n+1)\pi+\theta,n\in\mathbb{Z}\} (C){x∣(2n−1)π+θ<x<2nπ−θ,n∈Z}\text{(C)}\{x|(2n-1)\pi+\theta<x<2n\pi-\theta,n\in\mathbb{Z}\} (D){x∣(2n−1)π−θ<x<2nπ+θ,n∈Z}\text{(D)}\{x|(2n-1)\pi-\theta<x<2n\pi+\theta,n\in\mathbb{Z}\}
Back to ProblemsView on AoPS