Free · Mathematical relationships

Sine of an Angle and Principal Inverse

Sine is the signed vertical coordinate on the unit circle. The inverse returns the principal angle between −90° and 90°; it does not recover every periodic solution.

Formula & worked example
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How to use this calculator

Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

With angle = 30, sine = 0.5.

s = sin(θ); θ = arcsin(s)

Worked example

Enter these known values and leave the other values blank.

Angle: 30 deg

Sine: 0.5

Assumptions and limitations

Sine is the signed vertical coordinate on the unit circle. The inverse returns the principal angle between −90° and 90°; it does not recover every periodic solution.
Enter enough independent values and clear the quantity being solved. Locks preserve known values; contradictory inputs can make the system inconsistent. Unit controls convert physical quantities rather than merely changing their labels.
Displayed precision is numerical rounding, not an estimate of measurement uncertainty.

Common questions

How do I solve for a missing quantity?

Clear the missing value, enter the independent known values and retain compatible units. A nonunique inverse may require another known value.

What relationship is used?