Inverse Trig (arcsin, arccos, arctan) Calculator
Find the angle in degrees whose sine, cosine or tangent equals a given value. This inverse-trig calculator returns the principal arcsine, arccosine and arctangent for any number you enter.
Enter Values
How to use this calculator
- Enter any real number in the Value field (it can be negative).
- Read the arctangent, which is defined for every value.
- Check the arcsine and arccosine — these are only defined when the value is between -1 and 1.
How it works
The calculator applies the inverse trig functions and converts the resulting radians to degrees. Arctangent accepts any real input and returns a principal angle between -90° and 90°. Arcsine also returns -90° to 90°, and arccosine returns 0° to 180°, but both require an input in the range -1 to 1 (the range of sine and cosine); outside that range they are shown as undefined.
Worked example
Worked example. For a value of 0.5: arctangent = 26.57°, arcsine = 30° and arccosine = 60°. For a value of 2, only the arctangent (63.43°) is defined; arcsine and arccosine are undefined.
Common mistakes
- Expecting an arcsine or arccosine for values above 1 or below -1 — those inputs are outside the domain and return undefined.
- Forgetting that these are principal values, so many other angles share the same sine, cosine or tangent.
- Reading the results as radians; every angle here is given in degrees.
Frequently asked questions
Why are arcsine and arccosine undefined for a value of 2?
Sine and cosine only ever produce outputs between -1 and 1, so there is no angle whose sine or cosine equals 2. Only arctangent is defined for all real numbers.
What are principal values?
Because trig functions repeat, each inverse returns one standard angle: arcsine and arctangent between -90° and 90°, and arccosine between 0° and 180°.
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Tip: Enter any known values to calculate the remaining results.
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