How this calculator works
Sine tracks vertical position around the unit circle. It starts at zero, rises to one at 90°, returns to zero at 180° and reaches minus one at 270°. The standard-angle table supplies points for a sine graph without drawing a continuous curve. This tool evaluates the basic function with amplitude one and period one turn. Multiplying by A changes amplitude; multiplying the angle by B changes the period. Ratio mode returns arcsine on [-90°, 90°].
Formula
sin θ = opposite/hypotenuse = unit-circle y. sin(θ+2π)=sin θ; sin(-θ)=-sin θ. For y=A sin(Bx+C)+D: amplitude=|A| and period=2π/|B| when B≠0.
Worked example
sin 30°=1/2, while sin 270°=-1. A wave y=3 sin(2x) would have amplitude 3 and period π radians; its value at x=30° is 3√3/2.
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Frequently asked questions
Is sine measured in degrees?
The input angle has angular units, but the sine value is a dimensionless ratio. Select the angle unit beside the input.
Why are 30° and 150° both mapped to 0.5?
Their unit-circle points have the same height. Sine symmetry gives sin(180°-θ)=sin θ.
Does sine have an amplitude?
The basic function has amplitude 1. For a scaled sine wave, amplitude is the absolute value of the coefficient outside sine.