Inverse Cosine Calculator
Trigonometric inverse cosine calculator
Result for cos−1(0.5)
60 ° (degrees)
1.0471975511966 rad (radians)
# What is inverse cosine
Inverse cosine is the inverse of the basic cosine function. In the cosine function, the value of angle θ is taken to give the ratio adjacent/hypotenuse. However, the inverse cosine function takes the ratio adjacent/hypotenuse and gives angle θ.
cos-1 (adjacent/hypotenuse) = θ
Inverse cosine symbol
Inverse cosine is represented as cos-1 or arccos.
# Inverse cosine rule
The rule for inverse cosine is derived from the rule of the cosine function.
a2 = b2 + c2 - 2bc cos(A)
Rearraning the equation to get cos-1 rule:
a2 - b2 - c2 = -2bc cos(A)
a2 - b2 - c2 / 2bc = cos(A)
cos-1 (a2 - b2 - c2 / 2bc)
# Arccos table
| x | Deg. Degrees | Rad. Radians |
|---|---|---|
| arccos(-1.0) | 180.00 |
3.14
π |
| arccos(-0.9) | 154.15 | 2.69 |
| arccos(-0.8) | 143.13 | 2.49 |
| arccos(-0.7) | 134.42 | 2.34 |
| arccos(-0.6) | 126.86 | 2.21 |
| arccos(-0.5) | 120.00 |
2.09
2π / 3 |
| arccos(-0.4) | 113.57 | 1.98 |
| arccos(-0.3) | 107.45 | 1.87 |
| arccos(-0.2) | 101.53 | 1.77 |
| arccos(-0.1) | 95.73 | 1.67 |
| arccos(0.0) | 90.00 |
1.57
π / 2 |
| arccos(0.1) | 84.26 | 1.47 |
| arccos(0.2) | 78.46 | 1.36 |
| arccos(0.3) | 72.54 | 1.26 |
| arccos(0.4) | 66.42 | 1.15 |
| arccos(0.5) | 60.00 |
1.04
π / 3 |
| arccos(0.6) | 53.13 | 0.92 |
| arccos(0.7) | 45.57 | 0.79 |
| arccos(0.8) | 36.86 | 0.64 |
| arccos(0.9) | 25.84 | 0.45 |
| arccos(1.0) | 0.00 | 0.00 |