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Calculate the inverse sine (arcsin) of a value. Find the angle whose sine equals the input value.
| x | arcsin(x) in Degrees | arcsin(x) in Radians |
|---|---|---|
| -1 | -90° | -π/2 |
| -0.866 | -60° | -π/3 |
| -0.707 | -45° | -π/4 |
| -0.5 | -30° | -π/6 |
| 0 | 0° | 0 |
| 0.5 | 30° | π/6 |
| 0.707 | 45° | π/4 |
| 0.866 | 60° | π/3 |
| 1 | 90° | π/2 |
y = arcsin(x) means sin(y) = x
d/dx[arcsin(x)] = 1/√(1-x²)
Odd function: arcsin(-x) = -arcsin(x)
arcsin(x) + arccos(x) = π/2
Because sine gives the same value for infinitely many angles, we need to restrict the output to make the inverse a function. The interval [-π/2, π/2] is called the principal value range.
Use the reference angle. If you need an angle in Quadrant II, use 180° - arcsin(x). For other quadrants, use symmetry properties.
They're the same thing! Both notations mean the inverse sine function. Note that sin⁻¹(x) ≠ 1/sin(x); that would be csc(x).