What does the graph of y = cos x look like?
It is a smooth wave identical in shape to the sine curve but starting at its maximum. At x = 0 it is 1, falls to 0 at 90°, reaches −1 at 180°, returns to 0 at 270°, and back to 1 at 360°.
// maths › Trigonometric Functions & Graphs
y = cos x
Plot and evaluate the cosine function y = cos x, seeing its amplitude, period, and range in degrees or radians, with a linked animation where a point moving around the unit circle traces the cosine wave so you can see why it leads the sine curve by ninety degrees.
y = cos x (amplitude 1, period 360° = 2π)
Angle unit
Frequently asked questions
How is the cosine graph related to the sine graph?
The cosine curve is the sine curve shifted 90° to the left: cos x = sin(x + 90°). They share the same amplitude, period, and range.
Can you give a worked example?
At x = 60°, y = cos 60° = 0.5, so the point (60°, 0.5) lies on the curve. The same angle in radians is 60° = π/3 ≈ 1.0472 rad; the Degrees/Radians toggle marks the x-axis in multiples of π.
What are its amplitude and period?
Amplitude 1 (it ranges between −1 and 1) and period 360° or 2π radians, after which the wave repeats exactly.
Where is this used in real life?
Cosine waves model alternating current, sound and light, and any oscillation that starts at a peak; engineers use them for signal analysis, and they describe seasonal cycles and circular motion.