Inverse Trigonometric Functions Calculator

Inverse trigonometric functions recover an angle from a known trigonometric ratio. Ordinary sine, cosine, and tangent start with an angle and produce a number. Their inverse functions reverse that direction: arcsine starts with a sine ratio, arccosine starts with a cosine ratio, and arctangent starts with a tangent ratio. These operations are essential when a right triangle provides side lengths but the missing quantity is an angle. They also appear throughout navigation, surveying, physics, computer graphics, signal processing, and engineering. Each inverse function returns a principal value because infinitely many angles can share the same trigonometric ratio. Arcsine returns an angle from negative pi over two through positive pi over two. Arccosine returns an angle from zero through pi. Arctangent returns an angle strictly between negative pi over two and positive pi over two. This calculator uses those standard principal branches. Arccotangent is defined here with a principal range from zero through pi, using the two-argument arctangent convention so negative inputs produce an angle in the second quadrant. The reciprocal functions follow directly from the primary functions. Arccosecant of a value is arcsine of its reciprocal, while arcsecant is arccosine of its reciprocal. Consequently, arcsine and arccosine accept values from negative one through one. Arccosecant and arcsecant accept values whose absolute magnitude is at least one. Arctangent and arccotangent accept every finite real number. Domain checking matters because values outside these ranges do not correspond to real angles. Results are displayed in both radians and degrees. Radians are the natural unit for calculus and most programming libraries because they measure an angle through arc length. Degrees divide a complete turn into 360 familiar units and are often easier to interpret in geometry or practical measurement. The conversion is degrees equals radians multiplied by 180 and divided by pi. Keeping both forms visible prevents unit confusion and makes the answer useful in either classroom or technical work. To interpret a result, remember that the calculator returns one representative angle, not every coterminal or periodic solution. For an equation involving sine, cosine, or tangent, additional solutions may be found from symmetry and the function's period. Use the principal result as the starting point, then apply the relevant identities for the interval in your problem. The calculator preserves enough decimal precision for common mathematical and engineering work while presenting a readable rounded value.