Properties of sin(2x)

Problem

We are given the function \(f: x\mapsto \sin(2x)\) defined on \(\mathbb{R}\). What are the amplitude, period, and its range.

Solution

The sine function has amplitude 1, period \(2\pi\) and the range \([-1, 1]\). The given function \(f\) has the same amplitude and range. Due the factor of 2 in the argument, its period is only \(\pi\).

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