Math Playground
Algebra

Sin, cos, tan graphs

The waves trigonometry draws when you sweep an angle.

Sweep an angle around the unit circle and the y-coordinate traces sin, the x-coordinate traces cos.

Drag the sliders
-6-24
y = c·sin(a·x + b)
Wave lab — drag the sliders, watch it move
λ

wave speed v = f λ = 0.50 × 120 = 60 px/s

Reading y = c·sin(a·x + b)

  • c stretches it vertically — the amplitude (height of a peak above the midline).
  • a squeezes it horizontally — bigger a ⇒ shorter period = 2π / a.
  • b slides it left/right — the phase shift. Drag the sliders and watch each one act.
Your turn

What is the period and amplitude of y = 3 sin(2x)?

Sound, light, alternating current, tides, radio — every wave is one of these curves, or a sum of them (that's Fourier analysis). The three knobs above are loudness, pitch, and timing.

Key features

  • Period of sin and cos: 2π (360°).
  • Amplitude: 1 for sin and cos.
  • tan: period π, vertical asymptotes at ±π/2.