Inverse Trigonometric Functions Calculator
Calculate arcsin, arccos, arctan (sin⁻¹, cos⁻¹, tan⁻¹) to find angles from trig ratios. Returns principal values in degrees and radians. Includes all inverse trig functions.
Formula & Reference
| Variable | Symbol | Formula | Units |
|---|---|---|---|
| Inverse Trigonometric Functions Calculator | — | θ = arcsin(x), arccos(x), arctan(x) | degrees / radians |
Step-by-Step Examples
arcsin(0.5)=?
- sin(θ)=0.5 → θ=30°
- arcsin returns principal value in [−90°,90°]
arctan(1)=?
- tan(θ)=1 → θ=45°
- arctan returns value in (−90°,90°)
arccos(0)=?
- cos(θ)=0 → θ=90°
- arccos range is [0°,180°]
Real-World Applications
Common Mistakes to Avoid
arcsin(2) is undefined — sine never exceeds 1. arctan accepts any real number.
arcsin returns one value (principal). All angles with the same sine: θ and π−θ. Always check which quadrant you need.
atan(y/x) can't distinguish (1,2) from (−1,−2). atan2(y,x) gives correct angle in all four quadrants.
Frequently Asked Questions
Related Math Calculators
Formula Explorer connections
Interpretation: This relationship connects dimensions, coordinates, angles or trigonometric ratios to a geometric measurement. Assumption: Use a consistent angle mode and length unit, identify the intended shape or coordinate system, and verify that the supplied dimensions form valid geometry.