Inverse Cosine Calculator – Calculate arccos(x)
Find the angle in degrees or radians using the inverse cosine with the arccos calculator below.
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How to Find Arccos
Arccos is a trigonometric function to calculate the inverse cosine. Arccos can also be expressed as cos-1(x).
Arccos is used to undo or reverse the cosine function. If you know the cosine of an angle, you can use arccos to calculate the angle.
Since arccos is the inverse of the cosine function, and many angles share the same cosine value, arccos is a periodic function. Each arccos value can result in multiple angle values. The primary result for arccos is known as the principal value and is the angle in the range of 0° to 180°.
To calculate arccos, use a scientific calculator and the acos function, or just use the calculator above. Most scientific calculators require the angle value in radians to solve for cos.
Inverse Cosine Formula
The inverse cosine formula is:
y = cos(x) | x = arccos(y)
Thus, if y is equal to the cosine of x, then x is equal to the arccos of y.
Inverse Cosine Graph
If you graph the arccos function for every possible value of cosine, it forms a curve from (-1, π) to (1, 0).
Because the value of cosine is always in the range of -1 to 1, the inverse cosine curve starts at x = -1 and ends at x = 1. Since the peak of the cosine wave is at 0 radians and the dip of the wave is at π radians, the y value ends at those points.
Inverse Cosine Table
The table below shows common cosine values and the arccos, or angle for each of them.
|Cosine||Angle (degrees)||Angle (radians)|
|–√6 + √2 / 4||165°||11π / 12|
|–√3 / 2||150°||5π / 6|
|–√2 / 2||135°||3π / 4|
|–1 / 2||120°||2π / 3|
|–√6 – √2 / 4||105°||7π / 12|
|0||90°||π / 2|
|√6 – √2 / 4||75°||5π / 12|
|1 / 2||60°||π / 3|
|√2 / 2||45°||π / 4|
|√3 / 2||30°||π / 6|
|√6 + √2 / 4||15°||π / 12|