Graph of y = cos(2x)
Interactive graph of y = cos(2x) (doubled frequency cosine). Explore how the argument coefficient compresses the cosine wave horizontally.
Loading graph...
Drag to pan, scroll to zoom, click on the curve to pin coordinates. Edit equations in the sidebar.
Understanding the Function
The function y = cos(2x) is a cosine wave with double the frequency of the standard cos(x). The factor of 2 inside the argument halves the period from 2*pi to pi, compressing the wave so that it completes two full oscillations in the same horizontal distance where cos(x) completes one. The amplitude remains 1.
Cosine waves at multiple frequencies combine according to trigonometric identities: cos(2x) = cos²(x) - sin²(x) = 1 - 2sin²(x) = 2cos²(x) - 1. These double-angle identities appear in Fourier analysis, AC power engineering (the power factor involves cos²), and computer graphics (rotation matrices use these identities to compose rotations efficiently).
Key properties: amplitude 1, period pi, zeros at x = pi/4 + n*pi/2 for integer n, maximum of 1 at x = n*pi, minimum of -1 at x = pi/2 + n*pi. The derivative is -2*sin(2x). Compared with sin(2x), this function is shifted left by pi/4 (a quarter of the compressed period).