Graph of y = sin(2x)
Interactive graph of y = sin(2x). Explore how multiplying the argument changes the frequency and period of the sine wave.
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Understanding the Function
The function y = sin(2x) is a sine wave with double the frequency of the standard sin(x). The coefficient 2 inside the argument compresses the wave horizontally, reducing its period from 2*pi to pi. The amplitude remains 1 since there is no vertical scaling.
Frequency scaling is one of the fundamental transformations in wave analysis. In music, doubling the frequency raises a pitch by one octave. In electronics, signal generators produce waves at specific frequencies for testing and communication. Understanding how the argument coefficient affects the period is essential for signal processing and Fourier analysis.
Key properties: amplitude 1, period pi (half of standard sine), frequency twice that of sin(x), zeros at x = n*pi/2 for every integer n, maximum of 1 at x = pi/4 + n*pi. The derivative is 2*cos(2x), showing that the rate of change also doubles.