This calculator finds inverse trigonometric values, the angle whose sine, cosine or tangent equals a number you enter, giving arcsin, arccos and arctan in both degrees and radians. Where the ordinary trig functions take an angle and give a ratio, the inverse functions go the other way: you know the ratio, such as the opposite over the hypotenuse, and you want the angle. This is exactly what you need to find an angle in a right triangle from its sides, to work out the angle of a ramp or roof from its rise and run, to recover a phase angle in physics, or to solve trigonometric equations. The three inverse functions have important domains. Arcsin and arccos only accept values between minus one and plus one, because sine and cosine never exceed that range, so this calculator flags values outside it. Arctan accepts any number, since the tangent can be any value. You enter a value, and the calculator returns arctan as the headline, with arcsin and arccos shown alongside, each in degrees, plus the radian equivalent. The results update as you type. Use it for trigonometry and geometry homework, for practical angle problems in building and surveying, or to check a calculation. A useful reminder: the inverse functions return the principal value, a single angle in a standard range, so in a real problem there may be other angles with the same ratio that you need to consider from the context. The calculations are exact for your input, rounded for display in degrees and radians.
Arcsin and arccos need a value between -1 and 1. Results are principal values. Shown in degrees and radians, rounded for display.
Each inverse function returns the angle whose sine, cosine or tangent equals your value. The calculator computes them and converts from radians to degrees by multiplying by 180 over pi. Arcsin and arccos are only defined for values from minus one to plus one; arctan is defined for all values.
For a value of 0.5, arcsin is 30 degrees, because the sine of 30 degrees is 0.5. Arccos is 60 degrees, since the cosine of 60 degrees is 0.5. Arctan is about 26.57 degrees, the angle whose tangent is 0.5, which in radians is about 0.4636.
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