Inverse Trig Calculator
The inverse trigonometric functions answer a simple question: if you know a ratio, what is the angle? The ordinary sine, cosine, and tangent functions take an angle and give you a ratio. The inverse functions go the other direction. Arcsin, arccos, and arctan take a ratio and give you the angle. This is exactly what you need when you have the sides of a right triangle and want the angle, when you know the slope of a ramp and want its angle from horizontal, or when you are solving an equation like sin(x) = 0.5 and need to find x. This calculator takes a single value and returns all three inverse trig results at once: arcsin and arccos in degrees, arctan in degrees, and arctan in radians. Arcsin and arccos only accept values between minus one and plus one because sine and cosine never go outside that range. Arctan accepts any value at all since the tangent can be any number. The results are principal values, meaning the single standard angle in a defined range: arcsin and arctan return between minus 90 and 90 degrees, while arccos returns between 0 and 180 degrees. In a real problem there may be other angles with the same ratio, and you need to use the context to find them. For a value of 0.5, arcsin returns 30 degrees, arccos returns 60 degrees, and arctan returns about 26.57 degrees. Enter any value and the results update instantly. The radian equivalent of arctan is shown alongside the degree result, and you can convert any angle using the degrees to radians calculator linked below.
Arcsin and arccos require a value between -1 and 1. Results are principal values. Rounded for display.
How it works
Each inverse function returns the angle whose sine, cosine or tangent equals your value. The calculator uses the JavaScript Math.asin(), Math.acos(), and Math.atan() functions, which work in radians, and converts to degrees by multiplying by 180 divided by pi. Arcsin and arccos are only defined for values from minus one to plus one; arctan is defined for all real numbers.
Worked example
For a value of 0.5: arcsin = 30 degrees because sin(30) = 0.5. Arccos = 60 degrees because cos(60) = 0.5. Arctan = 26.57 degrees because tan(26.57) = 0.5. In radians, arctan(0.5) = 0.4636. These match the pre-filled default above.
Related calculators
- Unit Circle Calculator: sine, cosine and tangent at any angle on the unit circle.
- SOHCAHTOA Calculator: solve right triangles from an angle and a side.
- Reference Angle Calculator: find the reference angle for any angle in any quadrant.
- Law of Sines and Cosines: solve non-right triangles.