Loading Calculator...
Please wait a moment
Please wait a moment
Calculate the inverse cosine (arccos) of a value. Find the angle whose cosine equals the input value.
| x | arccos(x) in Degrees | arccos(x) in Radians |
|---|---|---|
| -1 | 180° | π |
| -0.866 | 150° | 5π/6 |
| -0.707 | 135° | 3π/4 |
| -0.5 | 120° | 2π/3 |
| 0 | 90° | π/2 |
| 0.5 | 60° | π/3 |
| 0.707 | 45° | π/4 |
| 0.866 | 30° | π/6 |
| 1 | 0° | 0 |
y = arccos(x) means cos(y) = x
d/dx[arccos(x)] = -1/√(1-x²)
arccos(-x) = π - arccos(x)
arcsin(x) + arccos(x) = π/2
This range (Quadrants I and II) ensures each output is unique. Cosine is one-to-one on [0, π], so it has a well-defined inverse there.
They're complementary: arcsin(x) + arccos(x) = π/2 (90°). So arccos(x) = π/2 - arcsin(x).
Arccos only gives Q1 or Q2 angles. For other quadrants, use 360° - arccos(x) for Q4, or note that cosine is negative in Q3.