Inverse Trigonometric Calculator
Calculate inverse sine, inverse cosine, inverse tangent, or atan2 in degrees or radians with principal ranges, reference angles, quadrants, and checks.
Inverse Trigonometric Calculator inputs
Change the calculator-specific fields below. The result, checks, and visual update from this calculator’s own formula engine.
Inverse Trigonometric Calculator results
How the inverse trig calculator works
This page is built for the exact search intent represented by inverse trig calculator. It exposes the governing assumptions and supporting quantities instead of returning an unexplained headline number.
Inverse does not mean reciprocal
sin⁻¹(x) means the inverse sine or arcsine, not 1/sin(x). The inverse function returns an angle whose sine, cosine, or tangent equals the entered ratio. Reciprocal trigonometric functions are cosecant, secant, and cotangent.
Principal ranges and multiple angles
Inverse functions return one principal angle so they can behave as functions. A trigonometric equation can have additional coterminal or supplementary solutions. The calculator reports the common second solution in one 0–360-degree cycle for sine and cosine and makes the principal range explicit.
Why atan2 is different
atan2 uses both y and x, preserving the signs needed to identify the correct quadrant. Ordinary arctan(y/x) loses that quadrant information and fails when x is zero. Use atan2 for vectors, bearings, coordinate geometry, and programming calculations.
Reliable-use checklist
Confirm that the selected mode, units, signs, dates, rates, and definitions match the original problem. Retain the detailed output and supporting cards so the answer can be reproduced. Test a known example before relying on a custom case, and use current official or professional guidance when taxes, benefits, safety, contracts, or regulated decisions are involved.
The inverse trig calculator runs locally in the browser. It does not transmit entered values, create an account, or retain a calculation history. Full internal precision is kept during calculation and display rounding is applied only to readable outputs.
Inverse Trigonometric Calculator questions
Why does sin⁻¹ have a limited input range?
Real sine values are always between −1 and 1.
Why are calculator answers sometimes in radians?
The selected angle mode controls the display. Many calculus and programming contexts use radians.
What is atan2(1,−1)?
Its principal angle is 135 degrees, in quadrant II.