What does the graph of y = sin x look like?
It is a smooth wave that oscillates between −1 and 1. Starting at 0, it rises to a maximum of 1 at 90°, returns to 0 at 180°, drops to a minimum of −1 at 270°, and comes back to 0 at 360°, then repeats.
// maths › Trigonometric Functions & Graphs
y = sin x
Plot and evaluate the sine function y = sin 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 sine wave out in real time so you can see exactly why the curve has its shape.
y = sin x (amplitude 1, period 360° = 2π)
Angle unit
Frequently asked questions
What are its amplitude and period?
The amplitude is 1 — the curve reaches a maximum of 1 and a minimum of −1. The period is 360° (or 2π radians), meaning the whole pattern repeats every full turn.
Can you give a worked example?
At x = 30°, y = sin 30° = 0.5, so the point (30°, 0.5) lies on the curve. The same angle in radians is 30° = π/6 ≈ 0.5236 rad; switch the Degrees/Radians toggle and the x-axis is marked in multiples of π.
How does the unit circle make the wave?
The sine of an angle is the height of the matching point on the unit circle. As the point goes round, its height traces out the wave — which is why the curve rises and falls and repeats every 360°.
Where is this used in real life?
Sine waves model sound, light, radio signals, and alternating current; engineers use them for vibrations and oscillations, musicians and audio engineers for tones, and they describe tides, daylight hours, and many other naturally repeating patterns.